In number theory, 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...

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...

Fermat's little theorem, a property of prime numbers Fermat's theorem on sums of two squares, about primes expressible as a sum of squares Fermat's theorem...

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 is a...

remainder theorem, although it is not the significant part of that theorem. Although the original paper of Rivest, Shamir, and Adleman used Fermat's little theorem...

proof of Fermat's Last Theorem. Review of Fermat's Enigma by Andrew Bremner (1998), MR1491363. Radford, Tim (2 August 2013), "Fermat's Last Theorem by Simon...

theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Fermat's little theorem states that...

become Fermat numbers. It was while researching perfect numbers that he discovered Fermat's little theorem. He invented a factorization method—Fermat's factorization...

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. Wieferich...

referred to them in 1948 as numbers with the "Fermat property", or "F numbers" for short. Fermat's little theorem states that if p {\displaystyle p} is a prime...

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...

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...

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}...

where 23 = 1 + (2 × 11) and 89 = 1 + 4 × (2 × 11). Proof: By Fermat's little theorem, q is a factor of 2q−1 − 1. Since q is a factor of 2p − 1, for...

important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special...

..,({\tfrac {p-1}{2}})^{2}{\pmod {p}}.} As a is coprime to p, Fermat's little theorem says that a p − 1 ≡ 1 ( mod p ) , {\displaystyle a^{p-1}\equiv...

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...

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

The special case where n is prime is known as Fermat's little theorem. This follows from Lagrange's theorem and the fact that φ(n) is the order of the multiplicative...

satisfy the above equation which can be deduced from Fermat's little theorem. Fermat's theorem asserts that if p is prime, and coprime to a, then ap−1...

identities, Fermat's little theorem, Fermat's theorem on sums of two squares, and made distinct contributions to the Lagrange's four-square theorem. He also...

threefold Fermat quotient Fermat's difference quotient Fermat's factorization method Fermat's Last Theorem Fermat's little theorem Fermat's method Fermat's method...

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

may be computed using the extended Euclidean algorithm or using Fermat's little theorem as k q − 2 mod q {\displaystyle k^{q-2}{\bmod {\,}}q} . One can...

equation an + bn = cn has no positive integer solutions. Fermat's little theorem Fermat's little theorem field extension A field extension L/K is a pair of...

last, is a multiple of p {\displaystyle p} .[citation needed] By Fermat's little theorem, if p {\displaystyle p} is a prime number and x {\displaystyle...

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

Euclid–Euler theorem (number theory) Euler's theorem (number theory) Fermat's Last Theorem (number theory) Fermat's little theorem (number theory) Fermat's theorem...

multiplicative inverse based on Fermat's little theorem. Multiplicative inverse based on the Fermat's little theorem can also be interpreted using the...

{\displaystyle \sigma _{a}(\zeta )=\zeta ^{a}} . As a consequence of Fermat's little theorem, in the ring of p-adic integers Z p {\displaystyle \mathbb {Z}...