Fermat’s Last Theorem
Fermat’s Last Theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. It is among the most notable theorems in the history of mathematics and is considered one of the most important in number theory. Theorem was in the Guinness Book of World Records as the \”most difficult mathematical problem\” in part because the theorem has the largest number of unsuccessful proofs.
About Fermat’s Last Theorem in brief
Fermat’s Last Theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of Arithmetica. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995. It also proved much of the modularity theorem and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques. The connection is described below: any solution that could contradict Fermat’s Theorem could also be used to contradict the Taniyama–Shimura conjecture, which would follow automatically if it were true. Theorem was in the Guinness Book of World Records as the \”most difficult mathematical problem\” in part because the theorem has the largest number of unsuccessful proofs. The special case n = 4, proved by Fermat himself, is sufficient to establish that if the theorem is false for some exponent n that is not a prime number, it must also be true for some smaller n. The Pythagorean equation, x2 + y2 = z2, has an infinite number of positive integer solutions for x, y, and z; these solutions are known as Pythagorean triples. The proof for this equation was proved by Ernst Kummer in the mid-19th century and proved for all regular primes, leaving irregular primes to be analyzed individually.
In 1984, Gerhard Frey noticed an apparent link between these two previously unrelated and unsolved problems. The full proof that the two problems were closely linked was accomplished in 1986 by Ken Ribet, building on a partial proof by Jean-Pierre Serre, who proved all one part of the conjecture as the part known as the epsilon conjecture. Although both problems were widely considered to be daunting and daunting to solve, the proof was widely considered as well as well-received. The first proof of the Epsilon Conjecture was published in 1989. It was described as a \”stunning advance\” in the citation for Wiles’s Abel Prize award in 2016. It is among the most notable theorems in the history of mathematics and is considered one of the most important in number theory. It has been proved for only the primes 3, 5, and 7, although Sophie Germain innovated and proved an approach that was relevant to an entire class of primes. In 1955, Japanese mathematicians Goro Shimura and Yutaka TaniYama suspected a link might exist between elliptic curves and modular forms, two completely different areas of mathematics. This conjecture was widely seen as significant and important in its own right, but was widely considered completely inaccessible to proof. It stood on its own, with no apparent connection to Fermat’s Last The theorem.
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This page is based on the article Fermat’s Last Theorem published in Wikipedia (as of Dec. 05, 2020) and was automatically summarized using artificial intelligence.
