Class 3 - Residue Number System and Fermat’s Little Theorem | Notion

Introduction to Residue Number System
How many solutions to the congruence $x^2\equiv1(\text{mod }m)$ ?
State and Prove the Fermat’s Little Theorem

Exercises:

Find the value of $2^{20} + 3^{30}+4^{40}+5^{50}+6^{60}\text{ mod }7$.
It is known that numbers $p \text{ and } 8p^2+1$ are primes. Find $p$.