Fermat's Little theorem

In number theory Fermat's Little theorem states that for every prime and its coprime holds that:

$a^{p-1} = 1 \\;\\; in \\;\\; Z_{p}$

Proof of Fermat's little theorem

Fermat's Little theorem is a special case of Euler's theorem, which has been proven (see the proof).

Calculate $7^{35}$ in $Z_{17}$ .

$7^{35} = 7^{16} \\cdot 7^{16} \\cdot 7^{3} = 1 \\cdot 1 \\cdot 7^{2} \\cdot 7 = 49 \\cdot 7 = -2 \\cdot 7 = -14 = 3 \\;\\; in \\;\\; Z_{17}$

Here is the position ready for our customer's banners.