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  2. Proofs of Fermat's little theorem - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_Fermat's_little...

    Some of the proofs of Fermat's little theorem given below depend on two simplifications. The first is that we may assume that a is in the range 0 ≤ a ≤ p − 1 . This is a simple consequence of the laws of modular arithmetic ; we are simply saying that we may first reduce a modulo p .

  3. Proof of Fermat's Last Theorem for specific exponents

    en.wikipedia.org/wiki/Proof_of_Fermat's_Last...

    Fermat's Last Theorem states that no three positive integers (a, b, c) can satisfy the equation a n + b n = c n for any integer value of n greater than 2. (For n equal to 1, the equation is a linear equation and has a solution for every possible a and b.

  4. Gerhard Frey - Wikipedia

    en.wikipedia.org/wiki/Gerhard_Frey

    Gerhard Frey (German:; born 1 June 1944) is a German mathematician, known for his work in number theory.Following an original idea of Hellegouarch, [1] he developed the notion of Frey–Hellegouarch curves, a construction of an elliptic curve from a purported solution to the Fermat equation, that is central to Wiles's proof of Fermat's Last Theorem.

  5. Pseudoprime - Wikipedia

    en.wikipedia.org/wiki/Pseudoprime

    Fermat's little theorem states that if p is prime and a is coprime to p, then a p−1 − 1 is divisible by p. For an integer a > 1, if a composite integer x divides a x−1 − 1, then x is called a Fermat pseudoprime to base a. It follows that if x is a Fermat pseudoprime to base a, then x is coprime to a. Some sources use variations of this ...

  6. Fermat's little theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_little_theorem

    In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number a p − a is an integer multiple of p. In the notation of modular arithmetic , this is expressed as a p ≡ a ( mod p ) . {\displaystyle a^{p}\equiv a{\pmod {p}}.}

  7. Fermat's theorem (stationary points) - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem...

    Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.

  8. Fermat's theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem

    The works of the 17th-century mathematician Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions to a n + b n = c n; Fermat's little theorem, a property of prime numbers; Fermat's theorem on sums of two squares, about primes expressible as a sum of ...

  9. List of number theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_number_theory_topics

    Linear congruence theorem; Method of successive substitution; Chinese remainder theorem; Fermat's little theorem. Proofs of Fermat's little theorem; Fermat quotient; Euler's totient function. Noncototient; Nontotient; Euler's theorem; Wilson's theorem; Primitive root modulo n. Multiplicative order; Discrete logarithm; Quadratic residue. Euler's ...