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Fermat's little theorem was coined by Pierre de Fermat in 1640. **Fermat little theorem** states that

If p is a prime number, then for any integer a, the number a^{p} - a is an integer multiple of p.

In modular arithmetic it is expressed as

a^{p} = a (mod p)

For example, a = 3, p = 5, 3^{5} = 243, 243 - 3 = 240 = 5 x 48 is the integer multiple of 5.

If a is not divisible by p, Fermat's little theorem is equivalent to the statement that a^{p-1} - 1 is an integer multiple of p:

a^{p-1} = a (mod p)

For example, a = 3, p = 5, 3^{5-1} = 81 = 81 – 1 = 80 = 5 x 16

**Euler** given the proof for this theorem in 1736. Fermat theorem become one of the important fundamental result of **Elementary number theory**. Fermat little theorem is different from the Fermat last theorem (also called as Fermat conjecture)

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Daily Maths Topic Today - fermat little theorem.