Using Fermat's little theorem, find the least residue of the multiplicative inverse of 5^53 - 4 modulo 53.

Use Fermat’s little theorem to find the least residue of 863 modulo 31.

Let a be a natural number such that gcd(a, 10) = 1. Use Euler’s theorem to prove that a^40n+1 and a must have the same ones and tens digits in their base ten expansions

Combine Fermat’s Little Theorem with the Chinese Remainder Theorem to calculate the least residue of 3^1453 modulo 35.

What is order of 5^15 congruent to 6547(mod20143)?

3^69 (mod 23)  6^2003 (mod 11)