In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b,...

divisible by p. Fermat's original statement was Tout nombre premier mesure infailliblement une des puissances − 1 {\displaystyle -1} de quelque progression...

font par les nombres, Les éléments arithmétiques, and a Latin translation of the Arithmetica of Diophantus (the very translation where Fermat wrote a margin...

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...

of magic squares, is named after him. He solved many problems created by Fermat and also discovered the cube property of the number 1729 (Ramanujan number)...

This article collects together a variety of proofs of Fermat's little theorem, which states that a p ≡ a ( mod p ) {\displaystyle a^{p}\equiv a{\pmod {p}}}...

premier p', 2p' − 1 est un nombre premier p", etc. Cette proposition a quelque analogie avec le théorème suivant, énoncé par Fermat, et dont Euler a montré...

in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Although not...

théorème de Fermat (1–60) 1828 Mémoire sur la détermination des fonctions Y et Z que satisfont à l'équation 4(X^n-1) = (X-1)(Y^2+-nZ^2), n étant un nombre premier...

31, 39, 47, 55, 60, 63, 71 ... (sequence A004215 in the OEIS). Pierre de Fermat gave a criterion for numbers of the form 8a + 1 and 8a + 3 to be sums...

such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1...

nombres entiers, de l'équation xm=y2+1", Nouvelles annales de mathématiques, 1re série, 9: 178–181 Ribenboim, Paulo (1979), 13 Lectures on Fermat's Last...

second edition of the Théorie des Nombres, where he calls it très ingénieuse ("very ingenious"). See also Her work on Fermat's Last Theorem below. Germain's...

Pierre de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler). Fermat also investigated the primality of the Fermat numbers...

solutions to the equation x p + y p = z p {\displaystyle x^{p}+y^{p}=z^{p}} of Fermat's Last Theorem for odd prime p {\displaystyle p} . Specifically, Sophie Germain...

banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed...

mathematical star. One of his great successes at that time was the proof of Fermat's polygonal number theorem. He quit his engineering job, and received a one-year...

2307/2005976, JSTOR 2005976 Dusart, Pierre (1998), Autour de la fonction qui compte le nombre de nombres premiers (PDF) (PhD thesis) (in French) Dusart, Pierre...

and 9,437,056 along with Descartes (1636). 1637 – Pierre de Fermat claims to have proven Fermat's Last Theorem in his copy of Diophantus' Arithmetica. 1637 –...

17, 19, 23, 29, 37, 41, 47, 53, ... (sequence A220627 in the OEIS) If a Fermat number F n = 2 2 n + 1 {\displaystyle F_{n}=2^{2^{n}}+1} is prime, it is...

modular forms. This connection would ultimately lead to the first proof of Fermat's Last Theorem in number theory through algebraic geometry techniques of...

7, 2016 due to a server error. First detected as a probable prime using Fermat primality test on an Nvidia A100 GPU on October 11, 2024 Stillwell, John...

theorem was conjectured in Bachet's 1621 edition of Diophantus's Arithmetica; Fermat claimed to have a proof, but did not publish it. Over the years various...

Lectures on Fermat's Last Theorem, Springer-Verlag, p. 236, ISBN 978-0-387-90432-0, Zbl 0456.10006 Langevin, Michel (1977), "Quelques applications de nouveaux...

multiplication. The book anticipated the works of later mathematicians such as Fermat and Euler. The book examines several topics in number theory, among them...

théorème nouveau concernant les nombres premiers" (Proof of a new theorem concerning prime numbers), Nouveaux Mémoires de l'Académie Royale des Sciences...

angle de divergence par une fraction reflétant le nombre de tours par feuille ([...]), on tombe régulièrement sur un des nombres de la suite de Fibonacci...

Mirimanoff, "Sur les nombres de Bernoulli," L'Enseignement Mathématique 36 (1937), pp. 228–235 [5]. Paulo Ribenboim, 13 Lectures on Fermat's Last Theorem, Springer...

numbers modulo an integer—modular arithmetic—in his generalization of Fermat's little theorem. These investigations were taken much further by Carl Friedrich...

Chapter XXV Hellegouarch, Yves (2001). Invitation aux mathématiques de Fermat-Wiles. Paris: Dunod. ISBN 978-2-10-005508-1. Husemöller, Dale (2004)....