Euler's totient theorem

In number theory, Euler's totient theorem (also known as the Fermat–Euler theorem) states that if "n" and "a" are coprime, (meaning that the only number that divides "n" and "a" is 1), then the following equivalence relation holds:
where formula_2 is Euler's totient function.
Euler's theorem is a more refined theorem of Fermat's little theorem, which Pierre de Fermat had published in 1640, a hundred years prior. Fermat's theorem remained unproven until the work of 18th-century Swiss mathematician Leonhard Euler.