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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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

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}...

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...

..,({\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...

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...

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...

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...

= 2 × 4 + 3, so 23 divides 211 − 1. Proof: Let q be 2p + 1. By Fermat's little theorem, 22p ≡ 1 (mod q), so either 2p ≡ 1 (mod q) or 2p ≡ −1 (mod q)....

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...

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...

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

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...

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...

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...

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...

{\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}...