Fermat's Theorem and Wilson's Theorem

Fermat’s Theorem :- If n is a prime number, then m^n mod n = m implies that
m^(n-1) mod n = 1.

Wilson’s Theorem :- If n is a prime number, then
(n-1)! mod n = n-1, and, (n-2)! mod n = 1.

Any single digit number written (p-1) time is divisible by p, where p is a prime number greater than 5. Ex: - 222222 mod 7 =0.

       Any number, co prime to 100, when raised to power 20 and divided by 100, leaves remainder 1.