Fermat's little theorem proof by Euler
Firstly, $1^p - 1 = 0$. Now, try evaluating $2^p - 2$.
$$2^p - 2 = (1+1)^p - (1+1) = (1^p+1) - (1+1) = 1^p - 1 = 0$$ Rinse and repeat.
Firstly, $1^p - 1 = 0$. Now, try evaluating $2^p - 2$.
$$2^p - 2 = (1+1)^p - (1+1) = (1^p+1) - (1+1) = 1^p - 1 = 0$$ Rinse and repeat.