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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.
Fermat's Last Theorem is a theorem in number theory, originally stated by Pierre de Fermat in 1637 and proven by Andrew Wiles in 1995. The statement of the theorem involves an integer exponent n larger than 2.
Andrew Wiles in front of the statue of Pierre de Fermat in Beaumont-de-Lomagne in 1995, Fermat's birthplace in southern France. Wiles's proof of Fermat's Last Theorem has stood up to the scrutiny of the world's other mathematical experts. Wiles was interviewed for an episode of the BBC documentary series Horizon [27] about
The Correspondence of Pierre de Fermat in EMLO; History of Fermat's Last Theorem (French) The Life and times of Pierre de Fermat (1601–1665) from W. W. Rouse Ball's History of Mathematics; O'Connor, John J.; Robertson, Edmund F., "Pierre de Fermat", MacTutor History of Mathematics Archive, University of St Andrews
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 was conjectured by Pierre de Fermat in the 1600s, states the impossibility of finding solutions in positive integers for the equation + = with >. Fermat himself gave a proof for the n = 4 case using his technique of infinite descent , and other special cases were subsequently proved, but the general case was not proven ...
No Fermat prime can be expressed as the difference of two pth powers, where p is an odd prime. With the exception of F 0 and F 1, the last decimal digit of a Fermat number is 7. The sum of the reciprocals of all the Fermat numbers (sequence A051158 in the OEIS) is irrational. (Solomon W. Golomb, 1963)