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}}}...

Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In the notation of...

Leonhard Euler published a proof of Fermat's little theorem (stated by Fermat without proof), which is the restriction of Euler's theorem to the case where n...

person; this provides a digital signature. The proof of the correctness of RSA is based on Fermat's little theorem, stating that ap − 1 ≡ 1 (mod p) for any...

h(x)=x^{p-1}-1.} h also has degree p − 1 and leading term xp − 1. Modulo p, Fermat's little theorem says it also has the same p − 1 roots, 1, 2, ..., p − 1. Finally...

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}...

theorem does not hold for algebraic integers. This failure of unique factorization is one of the reasons for the difficulty of the proof of Fermat's Last...

general proof, various proofs were devised for particular values of the exponent n. Several of these proofs are described below, including Fermat's proof in...

nested proofs, or with their proofs presented after the proof of the theorem. Corollaries to a theorem are either presented between the theorem and the...

Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's Last Theorem, first conjectured...

his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus'...

11). Proof: By Fermat's little theorem, q is a factor of 2q−1 − 1. Since q is a factor of 2p − 1, for all positive integers c, q is also a factor of 2pc...

Eric W. "Fermat's Polygonal Number Theorem". MathWorld. Heath, Sir Thomas Little (1910), Diophantus of Alexandria; a study in the history of Greek algebra...

used to prove Fermat's little theorem and its generalization, Euler's theorem. These special cases were known long before the general theorem was proved...

congruence theorem Successive over-relaxation Chinese remainder theorem Fermat's little theorem Proofs of Fermat's little theorem Fermat quotient Euler's...

second factor zero, or they would not satisfy Fermat's little theorem. This is Euler's criterion. This proof only uses the fact that any congruence k x ≡...

numbers are prime. Indeed, the first five Fermat numbers F0, ..., F4 are easily shown to be prime. Fermat's conjecture was refuted by Leonhard Euler in...

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

observations of rubber, in Ecuador. Leonhard Euler produces the first published proof of Fermat's "little theorem". Sir Isaac Newton's Method of Fluxions...

In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that...

The proofs include: Six proofs of the infinitude of the primes, including Euclid's and Furstenberg's Proof of Bertrand's postulate Fermat's theorem on...

list of articles with mathematical proofs: Bertrand's postulate and a proof Estimation of covariance matrices Fermat's little theorem and some proofs Gödel's...

theorem, an upper bound on intersecting families of sets, proven by Gyula O. H. Katona using a double counting inequality. Proofs of Fermat's little theorem...

short proof of Fermat's Last Theorem for n ≥ 6 {\displaystyle n\geq 6} . The Fermat–Catalan conjecture, a generalization of Fermat's Last Theorem concerning...

incorrect (or no) proofs? Moritz. Theorems demoted back to conjectures Mei Zhang, Proofs shown to be wrong after formalization with proof assistant Steven-Owen...

subject. He proved Fermat's assertions, including Fermat's little theorem; made initial work towards a proof that every integer is the sum of four squares;...

"golden theorem". He published six proofs for it, and two more were found in his posthumous papers. There are now over 240 published proofs. The shortest...

correspond to a log-n-step loop. Because of that, proofs using prefix induction are "more feasibly constructive" than proofs using predecessor induction. Predecessor...

representatives of aperiodic necklaces. Lyndon word Inversion (discrete mathematics) Necklace problem Necklace splitting problem Permutation Proofs of Fermat's little...

proved in 2025. Multiple proofs of the theorem have been published. Steiner's proof uses Pappus chains and Viviani's theorem. Proofs by Philip Beecroft and...