• 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...
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  • 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...
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  • 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...
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  • 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...
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  • 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...
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  • 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...
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  • 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...
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  • Thumbnail for Pierre de Fermat
    become Fermat numbers. It was while researching perfect numbers that he discovered Fermat's little theorem. He invented a factorization method—Fermat's factorization...
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  • 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...
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  • Thumbnail for Carmichael number
    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...
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  • 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...
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  • 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...
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  • 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}...
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  • 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...
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  • Thumbnail for Modular arithmetic
    important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special...
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  • ..,({\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...
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  • 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...
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  • Thumbnail for Prime number
    de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler). Fermat also investigated the primality of the Fermat numbers...
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  • Thumbnail for Euler's totient function
    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...
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  • 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...
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  • 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...
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  • 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...
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  • congruence theorem Method of successive substitution Chinese remainder theorem Fermat's little theorem Proofs of Fermat's little theorem Fermat quotient...
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  • 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...
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  • 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...
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  • 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...
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  • Thumbnail for Number theory
    number theory includes the following: Proofs for Fermat's statements. This includes Fermat's little theorem (generalised by Euler to non-prime moduli); the...
    95 KB (12,176 words) - 01:01, 28 May 2025
  • 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...
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  • multiplicative inverse based on Fermat's little theorem. Multiplicative inverse based on the Fermat's little theorem can also be interpreted using the...
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  • {\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}...
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