The tutor introduces Fermat’s Theorem with a first example.

Fermat’s Theorem states that, for a prime number p and a number b not a multiple of p,

b^p-1 ≡ 1 (mod p).

(See my post here for a working definition of mod.)

This theorem is very useful for solving the following type of question:

Example: Give the remainder when 16^70 is divided by 71.

Solution: 71 is prime, and 16 is clearly not a multiple of it. Therefore, by Fermat’s Theorem,

16^70 ≡ 1 (mod 71)

Therefore, the remainder when 16^70 is divided by 71 is 1.

Source:

Dudley, Underwood. Elementary Number Theory. New York: W H Freeman and Company, 1978.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.