A generalization of Fermat's Little Theorem: for any integer a coprime to a positive integer n, a raised to Euler's totient function of n is congruent to 1 modulo n. It is foundational to modular arithmetic and to public-key cryptosystems such as RSA.
Facts
StatementFor coprime positive integers a and n, a raised to the power of Euler's totient function of n is congruent to 1 modulo n; the case where n is prime is Fermat's little theorem. 1 Connections
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Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
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Sources
1. Euler's Theorem (Totient) (Wikipedia)
Wikimedia Foundationlead paragraph, opening definition clause
In number theory, Euler's theorem (also known as the Fermat-Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers, then
lead section, history sentences
In 1736, Leonhard 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 prime number. Subsequently, Euler presented other proofs of the theorem, culminating with his paper of 1763, in which he proved a generalization to the case where n is not prime.
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