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Weisstein, Eric W. "Fermat's Last Theorem". MathWorld. O'Connor, John J.; Robertson, Edmund F. (1996), Fermat's last theorem, MacTutor History of Mathematical Topics, archived from the original on 2013-01-16 University of St Andrews. "The Proof". PBS. The title of one edition of the PBS television series NOVA, discusses Andrew Wiles's effort to ...
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a n + b n = c n for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. [1]
Fermat's Last Theorem, formulated in 1637, states that no three positive integers a, b, and c can satisfy the equation + = if n is an integer greater than two (n > 2).. Over time, this simple assertion became one of the most famous unproved claims in mathematics.
This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin. [6] The first successful proof was released in 1994 by Andrew Wiles , and formally published in 1995, after 358 years of effort by mathematicians.
The works of the 17th-century mathematician Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions to a n + b n = c n; Fermat's little theorem, a property of prime numbers; Fermat's theorem on sums of two squares, about primes expressible as a sum of ...
Fermat's last theorem in the case of exponent 3 states that the sum of two non-zero integer cubes does not result in a non-zero integer cube. The first recorded proof of the exponent 3 case was given by Euler. [3]
He invented a factorization method—Fermat's factorization method—and popularized the proof by infinite descent, which he used to prove Fermat's right triangle theorem which includes as a corollary Fermat's Last Theorem for the case n = 4. Fermat developed the two-square theorem, and the polygonal number theorem, which states that each ...
To prove the Fermat's Last Theorem for a strong irregular prime p is more difficult (since Kummer proved the first case of Fermat's Last Theorem for B-regular primes, Vandiver proved the first case of Fermat's Last Theorem for E-regular primes), the most difficult is that p is not only a strong irregular prime, but 2p + 1, 4p + 1, 8p + 1, 10p ...