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...

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...

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

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...

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...

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}...

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...

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

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...

..,({\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...

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...

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...

quotient is named after Pierre de Fermat. If the base a is coprime to the exponent p then Fermat's little theorem says that qp(a) will be an integer...

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...

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

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...

possibly composite. Édouard Lucas, for whom this test is named Fermat's little theorem Pocklington primality test, an improved version of this test which...

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...

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...

believed to be true. Fermat's Last Theorem was historically called a theorem, although, for centuries, it was only a conjecture. A theorem is a statement that...

1 ≡ 1 mod p {\textstyle g^{q}\equiv h^{p-1}\equiv 1\mod p} by Fermat's little theorem. Since g > 0 {\displaystyle g>0} and q {\displaystyle q} is prime...

in number theory, including the Chinese remainder theorem, Fermat's little theorem, and the Fermat primality test based on it. It also introduces calculation...

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

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

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...

in order to make such exceptions rare. Fermat's test for compositeness, which is based on Fermat's little theorem, works as follows: given an integer n...