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

where φ(n) is Euler's totient function. (The notation is explained in the article modular arithmetic.) In 1736, Leonhard Euler published his proof of Fermat's little theorem, which Fermat had presented without proof. Subsequently, Euler presented other proofs of the theorem, culminating with "Euler's theorem" in his paper of 1763, in which he attempted to find the smallest exponent for which Fermat's little theorem was always true.