# Euler's totient theorem facts for kids

In number theory, **Euler's totient theorem** (also known as the **Fermatâ€“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 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.

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