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Euler's theorem
Theorem on modular exponentiation
Euler's theorem
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 a φ ( n ) {\displaystyle a^{\varphi (n)}} is congruent to 1 {\displaystyle 1} modulo n, where φ {\displaystyle \varphi } denotes Euler's totient function; that is a φ ( n ) ≡ 1 ( mod n ) . {\displaystyle a^{\varphi (n)}\equiv 1{\pmod {n}}.} In 1736, Leonhard Euler published a proof of Fermat's little theorem (stated by Fermat without proof), which is the restriction of Euler...
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