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...

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}...

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...

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...

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...

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...

congruence theorem Method of successive substitution Chinese remainder theorem Fermat's little theorem Proofs of Fermat's little theorem Fermat quotient...

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'...

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...

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, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers. That is, every...

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...

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...

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...

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...

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

Probability Proofs of Fermat's little theorem Rodrigues' formula O'Connor, John J.; Robertson, Edmund F. "James Ivory". MacTutor History of Mathematics...

The Fermat primality test is a probabilistic test to determine whether a number is a probable prime. Fermat's little theorem states that if p is prime...

proof,: 458–462  reminiscent of one of the simplest proofs of Fermat's little theorem, can be obtained by evaluating the product Z = a ⋅ 2 a ⋅ 3 a ⋅...

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

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

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 ≡...

of a proof of Fermat's Last Theorem for the case n = 5, brought him immediate fame, being the first advance in the theorem since Fermat's own proof of...

consists of the p − 1 group elements σa, where σ a ( ζ ) = ζ a {\displaystyle \sigma _{a}(\zeta )=\zeta ^{a}} . As a consequence of Fermat's little theorem, in...

on number theory includes the following: Proofs for Fermat's statements. This includes Fermat's little theorem (generalised by Euler to non-prime moduli);...

produces the first published proof of Fermat's "little theorem". Sir Isaac Newton's Method of Fluxions (1671), describing his method of differential calculus...

Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against...