Kotaku. Luke Plunkett. Luke Plunkett is a Contributing Editor based in Canberra, Australia. He has written a book on cosplay, designed a game about airplanes, and also runs cosplay. The Straw Hat Pirates, mainly known as the Straw Hat Crew, is a pirate crew that originated from. The content of this page was created by users. It has not been screened or verified by IMDb staff. Watch Anime Dub List English Dubbed, Anime Dub List English Dubbed, Anime Dub List English Dubbed. Wells Fargo is already facing a blitz of litigation and regulatory scrutiny after the bank announced it would reimburse $80 million to 570,000 people who may have. Dasi super sari wali darty chudai dounlo ~ video bokep haylee le ~ b grade full nude movie tube ~ a j bailey bang brose hd ~ baljeet kaur wank tv ~ all full. Lyconroc will be getting a new Dusk Form in Pokémon Ultra Sun and Moon. It evolves from Rockruff at level 25 into slightly different forms depending on the version. Chris Guyot made this series of animated portraits from Overwatch. This looks like the best kids TV show that never was. Gmail is email that's intuitive, efficient, and useful. 15 GB of storage, less spam, and mobile access. Watch One Piece Episodes English Subbed & Dubbed at WatchOP: One Piece Episode 805 was postponed until September 17 2017 by Japan TV. :( Gomen! - Reason: Unknown Yet.
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The new Blade Runner movie is a terrifying glimpse of the near future. Titled Blade Runner 2049, it doesn’t hit theaters until October 6th, but these new. Laterite, an irreversibly indurated material, should not be confused with lateritic soils, which harden. These New Promo Shots From the Blade Runner Sequel Look Terrifyingly Real. The new Blade Runner movie is a terrifying glimpse of the near future. Titled Blade Runner 2. October 6th, but these new promotional shots look absolutely terrifying. In fact, the dystopian vision of the future that these images present looks all too real. The original Blade Runner had everything from enormous video screens to burning oil fields to serve as a helpful reminder of the fact that the movie was taking place in an advanced technological dystopia. The Columbia River is the largest river in the Pacific Northwest region of North America. The river rises in the Rocky Mountains of British Columbia, Canada. A batholith (from Greek bathos, depth + lithos, rock) is a large mass of intrusive igneous rock (also called plutonic rock) that forms from cooled magma deep in the. If you’re looking for a Yosemite map, you’ve come to the right place; currently I’ve collected 73 free Yosemite National Park maps to view and download. (PDF. Physical Geology, by Brian J. Skinner and Stephen C. Porter A well written introductory textbook on physical geology with lots of figures. The Solid Earth - An. And judging by these new promo shots, the sequel is every bit as scary. Ignore the captions to the photos. They’re probably a mistake. We all know that these are far too dystopian to be the world we actually live in today. Dead: Mitsubishi i- Mi. EVUnlike some other hatchbacks that will be departing the US market, I don’t predict anyone pouring one out for the Mitsubishi i- Mi. EV. The automaker announced will discontinue the electric vehicle due to slow sales. The next- generation Ford Fiesta may not be coming to the United States because you didn’t buy…Read more Green Car Reports got an official statement from Erica Rasch at Mitsubishi Motors North America who confirmed that “2. Mi. EV, and all available retail units have been sold.”According to Green Car Reports, the i- Mi. EV was technically the first mass- market electric car. Mitsubishi was testing fleets of them in Japan in 2. Tesla launched its roadster and the i- Mi. EV was on sale before the Nissan Leaf hit showrooms in 2. Despite its place in history, there weren’t too many positive qualities about the i- Mi. EV. It looked like an insect mated with a golf cart and had about the same amount of range. The i- Mi. EV would run out of juice in about 6. With the electric motors pumping out the equivalent of about 6. Mi. EV was also one of the slowest accelerating cars on the market doing the casual jaunt to 6. At the time, the i- Mi. EV was also the cheapest EV you could buy with a starting price of just under $3.
Mitsubishi will now focus its electric vehicle efforts on the Outlander Plug- In hybrid, which is the only crossover in its segment that offers a plug- in option, though no one seems to notice. Green Car Reports got an official statement from Erica Rasch at Mitsubishi Motors North America who confirmed that “2017 was the last model year for the i-MiEV, and. IMPORTANT SAFETY NOTICE Model 1500, 15LS Series Rifles by Howa Machinery Ltd. Howa Product Upgrade Registration. Howa Machinery, Ltd. of Japan continues to. Browse all new and used Springfield Rifles - Antique for sale and buy with confidence from Guns International. Now more than ever it’s important to be able to tell when you’re reading #FakeNews. However, determining whether something is fake or real isn’t always easy. President Donald Trump hates leaks. Well, he hates leaks about himself. The president is 100 percent fine with giving secrets to Russian officials in the Oval Office. Wouldn’t it be amazing if the Honda City Turbo and its Motocompo scooter were featured on Jason Drives? Hmmm. Instagram, Facebook’s hotter, snootier subsidiary, may have a massive data breach on its hands. This week, a security flaw within Instagram allowed hackers to. Get the latest News news with exclusive stories and pictures from Rolling Stone. Corvettes are dirty cars. I don’t care how many times they go to LeMans with the Z06, a Corvette will always remind me of Dirk Diggler, the 1970s, shag carpeting.The classic US stereotype of attempted Iranian ideological indoctrination via chants of “Death to America” and such has been old hat for quite some time. As noted. Statistical Techniques | Statistical Mechanics. Search the world's information, including webpages, images, videos and more. Google has many special features to help you find exactly what you're looking for. The Dirtiest Corvette Ever. Corvettes are dirty cars. I don’t care how many times they go to Le. Ever notice how Christopher Nolan’s movies (Interstellar, Inception, The Prestige) feel like an anxiety attack? Well, maybe that’s overstating things a bit. But. Mans with the Z0. Corvette will always remind me of Dirk Diggler, the 1. Even the new ones. Most owners I know embrace their heritage rocking excellent vintage mustaches and jewelry. They learned at an early age that gold goes well with a Corvette. I learned this as a kid too. I also learned that you never button your top three buttons when in the presence of a Corvette. You can’t let it know that you’re not cool. But this Corvette is different. It’s like someone shrank it into a little Miata and then turned it into a dune buggy! This is Brian Ballinger and Chris Smiths’s build for the next Gambler 5. Before we get into how great this is, lets get one thing out of the way. This is my least favorite Corvette model. It’s the one Barbie drove. It’s the Corvette most likely to enjoy the latest Michael Bolton album with its owner. Yet Brian turned it into heavy metal. You see this pull up and you pray he’s not here to pick up your daughter. No way Barbie would drive this. This is awesome. I actually don’t know that much about Corvettes but I can only assume that the factory gas tank was somewhere near the rear bumper and all the stuff that Brian cut off. I assume that’s why there is now a giant fuel cell dominating the back of the car. I also can’t help but see the desert racing dune buggy like stucture that’s been hiding under all that sports car. Amazing what a set of 3. Corvette. The mustache and mullet completes the look though. Brian and Chris call their creation the “Van Damme Vette” and it reminds me so much of my Baja Pig! The really cool part about their build is that its still on the factory suspension. They just cut away the bodywork instead of putting the wheels outside of it. Brian’s entering it in the Detroit Gambler next Spring and you can follow the build on Brian Ballinger’s and Chris Smith’s Facebook page. Maybe I should build a V8 powered Corvette? I asked why he started with the Corvette and “Free” was the answer. Oh, and with the one condition that we race it!” This is how the best racing stories start. I naturally suggested he cage it and run in the Baja 1. Brian’s response was, “It’s on my bucket list.”. Iran Has Pivoted to Video. The classic US stereotype of attempted Iranian ideological indoctrination via chants of “Death to America” and such has been old hat for quite some time. As noted by the New York Times on Saturday, in the past few years Iranian pro- government propaganda efforts have increasingly taken the form of rap videos glorifying the country’s military, spread on sites like local You. Tube equivalent Apparat and apps like Telegram. The Times rounded up some of the most high- profile attempts to appeal to the nation’s youth by pairing Iranian rappers with sweeping shots of military personnel and CGI- infused battle scenes, some of which are pretty over- the- top. They’re fascinating to watch, especially at a time when the current presidential administration has gone full hawk on Iran. They’re also more than a little uncomfortable, both because they show an oppressive government’s approach to a digitized era of propaganda and, if we’re being honest, they do kind of resemble pro- military media produced in places like the US. One video highlighted by the paper features Amir Tataloo, a musician with a “hard- partying, gangster- style reputation,” who extolled “our absolute right / to have an armed Persian gulf” while singing alongside naval personnel on the frigate Damavand. The Simpsons fans may notice a strong “Yvan Eht Nioj” vibe.)Another video from last year, titled “We Will Resist,” cost $2. US fighter jets bombing a mosque by a sunny beach, flanked by newly constructed oil refineries. A battalion of Iranian youth carrying flags retaliate by charging towards the water, conjuring up a gigantic tidal wave which sinks the US Navy’s Fifth Fleet. Another released in 2. Seraj Cyberspace Organization, which is affiliated with the Iranian Revolutionary Guards’ Basij volunteer militia, shows Iranian- backed fighters in Syria taking the fight to ISIS insurgents flying the terror group’s infamous black flag. The video features Hamid Zamani, who the Times noted was the mastermind behind the anti- imperialist song “USA.”“By Zaynab, we are the defenders of Damascus!” the singer croons as a sniper takes out an ISIS fighter in slow- motion. Husayn’s sister calls us to the Golden Shrine / How can the flames of death possibly set it ablaze?”Another Iranian propaganda effort highlighted by the Times was the 9. CGI action film Battle of the Persian Gulf II, which stars an animated version of Quds Force commander Gen. Qassem Suleimani annihilating US troops and naval forces.“The Americans threaten us, we want to say, ‘If you attack us, if you dare to do so, a rain of hot melted lead will be poured on you,” co- creator Farhad Azimi told the paper. The American aircraft carriers, vessels and warships will be sunk and converted into beautiful aquariums in the bed of the Persian Gulf.”So yeah, all this is unsettling. But again, lest Americans get too high on their horses about this, the US military- industrial complex, its marketing partners and Hollywood filmmakers have basically been doing higher- budget versions of the same thing for decades. One of the more obvious examples is the NFL, where flashy flyovers with high- tech military jets, troops marching with flags and even camouflage jersey sales have been a fixture for years, and the military has pumped tens of millions of dollars into patriotic displays at sports games. Others include the close relationship between the military and the video game industry, or its tight collaboration with the movie industry. Indications are strong President Donald Trump’s administration is seeking ways to back out of the US- Iran nuclear deal, per CNBC, which would set the stage for tensions to escalate rapidly—though with stakes a good bit realer than CGI tsunamis and bullet time. [New York Times]. Yahoo奇摩購物中心- 數十萬件商品8.
What is Mobirise? Mobirise is an offline app for Window and Mac to easily create small/medium websites, landing pages, online resumes and portfolios, promo sites for. Comment remonter tension night, salesforce com try, the world of djs and the turntable culture buy, da tweekaz get mad bite, home decor leather goodbye. Bundesliga - Wikipedia. The Bundesliga[ˈbʊndəsˌliːɡa] (lit. English: "Federal League", sometimes referred to as the Fußball- Bundesliga[ˈfuːsbal ˈbʊndəsˌliːɡa] or 1. The Bundesliga is composed of two divisions: the 1. Bundesliga (although it is rarely referred to with the First prefix), and, below that, the 2. 34. Spieltag, - 1. Bundesliga - Spielplan der Saison 2016/17. Bundesliga[ˈeːɐ̯stə ˈbʊndəsˌliːɡa]) is a professional association football league in Germany and the football league with the highest average stadium attendance worldwide. At the top of the German football league system, the Bundesliga is Germany's primary football competition. The Bundesliga comprises 1. Bundesliga. Seasons run from August to May. Most games are played on Saturdays and Sundays, with a few games played on weekdays. All of the Bundesliga clubs qualify for the DFB- Pokal. The winner of the Bundesliga qualifies for the DFL- Supercup. A total of 5. 4 clubs have competed in the Bundesliga since its founding. Die Bundesliga 2012/13 war die 50. Spielzeit der höchsten deutschen Spielklasse im Fußball der Männer. Sie startete am 24. August 2012 wie die erste Saison 1963/64. Fussball Nachrichten, Ergebnisse und Tabellen der 1. und 2. Bundesliga, sowie der 3. Liga und weiteren Ligen aus Deutschland präsentiert von RevierSport online. The 2011–12 Bundesliga was the 49th season of the Bundesliga, Germany's premier football league. The season started on 5 August 2011 with the opening match. Dieser Artikel behandelt die österreichische Fußball-Bundesliga der Herren. Für die österreichische Fußball-Bundesliga der Frauen siehe ÖFB Frauen Bundesliga. FC Bayern Munich has won the Bundesliga the most, winning the title 2. However, the Bundesliga has seen other champions with Borussia Dortmund, Hamburger SV, Werder Bremen, Borussia Mönchengladbach and Vf. B Stuttgart most prominent among them. The Bundesliga is one of the top national leagues, currently ranked second in Europe according to UEFA's league coefficient ranking, based on performances in European competitions over the past five seasons.[1] The Bundesliga is the number- one football league in the world in terms of average attendance; out of all sports, its average of 4. National Football League.[2] The Bundesliga is broadcast on television in over 2. The Bundesliga was founded in 1. Dortmund and the first season started in 1. The structure and organisation of the Bundesliga along with Germany's other football leagues have undergone frequent changes right up to the present day. The Bundesliga was founded by the Deutscher Fußball- Bund (English: German Football Association), but is now operated by the Deutsche Fußball Liga (English: German Football League). Overview[edit]. The winner of the Bundesliga receives the "Deutsche Meisterschale" (English: "German championship trophy")The Bundesliga is composed of two divisions: the 1. Bundesliga (although it is rarely referred to with the First prefix), and, below that, the 2. Bundesliga (2nd Bundesliga), which has been the second tier of German football since 1. The Bundesligen (plural) are professional leagues. Since 2. 00. 8, the 3. Liga (3rd League) in Germany has also been a professional league, but may not be called Bundesliga because the league is run by the German Football Association (DFB) and not, as are the two Bundesligen, by the German Football League (Deutsche Fußball- Liga or DFL). Below the level of the 3. Liga, leagues are generally subdivided on a regional basis. For example, the Regionalligen are currently made up of Nord (North), Nordost (Northeast), Süd (South), Südwest (Southwest) and West divisions. Below this are thirteen parallel divisions, most of which are called Oberligen (upper leagues) which represent federal states or large urban and geographical areas. The levels below the Oberligen differ between the local areas. The league structure has changed frequently and typically reflects the degree of participation in the sport in various parts of the country. In the early 1. 99. Germany and the subsequent integration of the national league of East Germany. Every team in the two Bundesligen must have a licence to play in the league, or else they are relegated into the regional leagues. To obtain a licence, teams must be financially healthy and meet certain standards of conduct as organisations. As in other national leagues, there are significant benefits to being in the top division: A greater share of television broadcast licence revenues goes to 1. Bundesliga sides. Bundesliga teams draw significantly greater levels of fan support. Average attendance in the first league is 4. Bundesliga. Greater exposure through television and higher attendance levels helps 1. Bundesliga teams attract the most lucrative sponsorships. Bundesliga teams develop substantial financial muscle through the combination of television and gate revenues, sponsorships and marketing of their team brands. This allows them to attract and retain skilled players from domestic and international sources and to construct first- class stadium facilities. The 1. Bundesliga is financially strong, and the 2. Bundesliga has begun to evolve in a similar direction, becoming more stable organizationally and financially, and reflecting an increasingly higher standard of professional play. Internationally, the most well- known German clubs include Bayern Munich, Borussia Dortmund, Schalke 0. Hamburger SV, Vf. B Stuttgart, Borussia Mönchengladbach, Werder Bremen and Bayer Leverkusen. Hamburger SV is the only club to have played continuously in the Bundesliga since its foundation. In the 2. 00. 8–0. Bundesliga reinstated an earlier German system of promotion and relegation, which had been in use from 1. The bottom two finishers in the Bundesliga are automatically relegated to the 2. Bundesliga, with the top two finishers in the 2. Bundesliga taking their places. The third- from- bottom club in the Bundesliga will play a two- legged tie with the third- place team from the 2. Bundesliga, with the winner taking up the final place in the following season's Bundesliga. From 1. 99. 2 until 2. Bundesliga had been automatically relegated, to be replaced by the top three finishers in the 2. Bundesliga. From 1. Bundesliga automatically, while promotion had been decided either completely or partially in promotion play- offs. The season starts in early August[4] and lasts until late May, with a winter break of six weeks (mid- December through to the end of January). In recent years, games have been played on Saturdays (five games beginning at 3: 3. Sundays (one game beginning at 3: 3. A new television deal in 2. Friday game (beginning at 8: 3. History[edit]Origins[edit]Prior to the formation of the Bundesliga, German football was played at an amateur level in a large number of sub- regional leagues until, in 1. Oberligen (Premier Leagues) remained. Regional champions and runners- up played a series of playoff matches for the right to compete in a final game for the national championship. On 2. 8 January 1. Deutscher Fußball Bund (DFB) had been founded in Leipzig with 8. The first recognised national championship team was Vf. B Leipzig, who beat DFC Prague 7–2 in a game played at Altona on 3. May 1. 90. 3. Through the 1. Germany's best players away from the semi- professional domestic leagues. At the international level the German game began to falter as German teams often fared poorly against professional teams from other countries. A key supporter of the central league concept was national team head coach Sepp Herberger who said, “If we want to remain competitive internationally, we have to raise our expectations at the national level.”Meanwhile, in East Germany, a separate league was established with the formation of the DS- Oberliga (Deutscher Sportausschuss Oberliga) in 1. The league was renamed the Football Oberliga DFV in 1. DDR- Liga or DDR- Oberliga. The league fielded 1. Foundation[edit]The defeat of the national team by Yugoslavia (0–1) in a 1. World Cup quarter- final game in Chile was one impetus (of many) towards the formation of a national league. At the annual DFB convention under new DFB president Hermann Gösmann (elected that very day) the Bundesliga was created in Dortmund at the Westfalenhallen on 2. July 1. 96. 2 to begin play starting with the 1. At the time, there were five Oberligen (Premier Leagues) in place representing West Germany's North, South, West, Southwest, and Berlin. East Germany, behind the Iron Curtain, maintained its separate league structure. Oberligen. From Oberliga Nord: Eintracht Braunschweig, Werder Bremen, Hamburger SVFrom Oberliga West: Borussia Dortmund, 1. FC Köln, Meidericher SV (now MSV Duisburg), Preußen Münster, Schalke 0. From Oberliga Südwest: 1. FC Kaiserslautern, 1. FC Saarbrücken. From Oberliga Süd: Eintracht Frankfurt, Karlsruher SC, 1. FC Nürnberg, TSV 1. München, Vf. B Stuttgart. Watch Movies Online Free in HD at Watch. The Prince and the.. Adventure,Family. Score: A Film Musi.. Documentary,Music. King of the Game. Action. 20. 01 Making Superman Fi.. Documentary,Short. 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Classes combine classic academic teaching with a case method approach with particular emphasis on utilising the presented material for improvement of students. This will include basic probabilistic modelling, decision tree construction and rollback, assessment of probabilities and ranges, sensitivity analysis, analysis of risk profiles and risk- attitudes, and application of decision analysis to litigation.(2) Game Theory involving interdependent decision- making under certainty and uncertainty. Course Catalog. This is a complete list of all Interskill courses grouped by curriculum. Courses are self-paced elearning, taken anytime, anywhere and in any order. This will include consideration of relevant case studies, sequential and simultaneous games, common cooperative and noncooperative games, dominant strategy, iterated dominance and Nash equilibria, information asymmetry, Akerlof. 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One of the features I've been working on for 1.6.0 is the ability to. There is an array with every element repeated twice except one. Find that element? In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: 1,1,2,3,5,8,1. His 1. 20. 2 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics. They are intimately connected with the golden ratio; for example, the closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5, .. Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings. Counting the different patterns of L and S of a given duration results in the Fibonacci numbers: the number of patterns that are m short syllables long is the Fibonacci number Fm + 1. AD), Gop. 1. 13. 5), and Hemachandra (c. He dates Pingala before 4. BC. 7. 00 AD), whose own work is lost, but is available in a quotation by Gopala (c. Variations of two earlier meters . For example, for . In this way, the process should be followed in all m. Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: a newly born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was: how many pairs will there be in one year? At the end of the first month, they mate, but there is still only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, and the female born two months ago also produces her first pair, making 5 pairs. At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs (which is the number of pairs in month n . This is the nth Fibonacci number. For example, out of the 1. F6 = 8 without consecutive 1s – they are 0. By symmetry, the number of strings of length n without consecutive 0s is also Fn+2. Equivalently, Fn+2 is the number of subsets S . The symmetric statement is: Fn+2 is the number of subsets S . For example, out of the 1. F5 = 5 without an odd number of consecutive 1s – they are 0. Equivalently, the number of subsets S . For example, out of the 1. F4 = 6 without an even number of consecutive 0s or 1s – they are 0. There is an equivalent statement about subsets. Relation to the golden ratio. It has become known as . In other words. This is the same as requiring a and b satisfy the system of equations. Therefore, it can be found by rounding, that is by the use of the nearest integer function: Fn=. For example, log. He wrote that . This can be derived from Binet's formula. For example, the initial values 3 and 2 generate the sequence 3, 2, 5, 7, 1. The ratio of consecutive terms in this sequence shows the same convergence towards the golden ratio. Another consequence is that the limit of the ratio of two Fibonacci numbers offset by a particular finite deviation in index corresponds to the golden ratio raised by that deviation. Or, in other words: limn. Uses the Fibonacci numbers 1, 1, 2, 3, 5, 8, 1. Decomposition of powers of the golden ratio. The resulting recurrence relationships yield Fibonacci numbers as the linear coefficients. As the eigenvalues of the matrix A are . The closed- form expression for the nth element in the Fibonacci series is therefore given by(Fn+1. Fn)=An(F1. F0)=S. The matrix representation gives the following closed expression for the Fibonacci numbers: (1. Fn+1. Fn. Fn. Fn. This matches the time for computing the nth Fibonacci number from the closed- form matrix formula, but with fewer redundant steps if one avoids recomputing an already computed Fibonacci number (recursion with memoization). This is true if and only if one or both of 5x. This can be taken as the definition of Fn, with the convention that F0 = 0, meaning no sum adds up to . Here, the order of the summand matters. For example, 1 + 2 and 2 + 1 are considered two different sums. For example, the recurrence relation. Fn=Fn. One group contains those sums whose first term is 1 and the other those sums whose first term is 2. In the first group the remaining terms add to n . So there are a total of Fn. In symbols. Specifically, the first group consists of those sums that start with 2, the second group those that start 1 + 2, the third 1 + 1 + 2, and so on, until the last group, which consists of the single sum where only 1's are used. The number of sums in the first group is F(n), F(n . So the total number of sums is F(n) + F(n . In this case note that Fibonacci rectangle of size Fn by F(n + 1) can be decomposed into squares of size Fn, Fn. Some of the most noteworthy are. The last is an identity for doubling n; other identities of this type are. F3n=2. Fn. 3+3. Fn. Fn+1. Fn. For example, we can write the sum of every odd- indexed reciprocal Fibonacci number as. Thus the Fibonacci sequence is an example of a divisibility sequence. In fact, the Fibonacci sequence satisfies the stronger divisibility property. If p is congruent to 1 or 4 (mod 5), then p divides Fp . The remaining case is that p = 5, and in this case p divides Fp. These cases can be combined into a single formula, using the Legendre symbol. If n is composite and satisfies the formula, then n is a Fibonacci pseudoprime. When m is large—say a 5. Fm (mod n) efficiently using the matrix form. Thus(Fm+1. Fm. Fm. Fm. The first few are: 2, 3, 5, 1. As there are arbitrarily long runs of composite numbers, there are therefore also arbitrarily long runs of composite Fibonacci numbers. No Fibonacci number greater than F6 = 8 is one greater or one less than a prime number. Mignotte, and S. Siksek proved that 8 and 1. Determining a general formula for the Pisano periods is an open problem, which includes as a subproblem a special instance of the problem of finding the multiplicative order of a modular integer or of an element in a finite field. However, for any particular n, the Pisano period may be found as an instance of cycle detection. Right triangles. The length of the longer leg of this triangle is equal to the sum of the three sides of the preceding triangle in this series of triangles, and the shorter leg is equal to the difference between the preceding bypassed Fibonacci number and the shorter leg of the preceding triangle. The first triangle in this series has sides of length 5, 4, and 3. Skipping 8, the next triangle has sides of length 1. Skipping 2. 1, the next triangle has sides of length 3. This series continues indefinitely. The triangle sides a, b, c can be calculated directly: an=F2n. As a consequence, for every integer d > 1 there are either 4 or 5 Fibonacci numbers with d decimal digits. More generally, in the base b representation, the number of digits in Fn is asymptotic to nlogb. Fibonacci sequence also can be connected to the field of economics. The procedure is illustrated in an example often referred to as the Brock–Mirman economic growth model. Yuri Matiyasevich was able to show that the Fibonacci numbers can be defined by a Diophantine equation, which led to his solving. Hilbert's tenth problem. This means that every positive integer can be written as a sum of Fibonacci numbers, where any one number is used once at most. |
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