Remainder Theorems Formulas Revision

For any integer $$a$$ and prime number $$p$$, $$a^p-a$$ is always divisible by $$p$$

For a prime $$p$$, remainder when $$(p-1)!$$ i divided by $$p$$ is $$(p-1)$$

If M and N are co-prime to each other then the remainder when $$M^{\phi(N)}$$ is divided by N is 1