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...

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...

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}}}...

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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

(1996). ""Bornes pour la torsion des courbes elliptiques sur les corps de nombres" [Bounds for the torsion of elliptic curves over number fields]". Inventiones...

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 –...

ranking is therefore provisional. First detected as a probable prime using Fermat primality test on an Nvidia A100 GPU on October 11, 2024 Stillwell, John...

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...

conjecture Proof of Fermat's Last Theorem for specific exponents Lebesgue–Nagell type equations Lebesgue, Victor-Amédée (1837), Thèses de mécanique et d'astronomie...

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...

This variation of the test is similar to the deterministic variant of the Fermat primality test. Both of these naïve variants are grossly inefficient and...

Papers of James Joseph Sylvester p. 590, tr. from "Sur les nombres dits de Hamilton", Compte Rendu de l'Association Française (Toulouse, 1887), pp. 164–168...

of its sides is the product of a power of two and any number of distinct Fermat primes (i.e. that the sufficient conditions given by Carl Friedrich Gauss...

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

of the LLL algorithm over euclidean rings or orders". Journal de Théorie des Nombres de Bordeaux. 8 (2): 387–396. doi:10.5802/jtnb.176. Cohen, Henri (2000)...