Thread: Compute 3^80 (mod 7)

I cannot remember how to do these problems and they are due right after break!!!
Compute 3 ^80 (mod7) and find all integers x such that 5x is congruent to 1 (mod 100)

#1: Note that:

So:

Multiply both sides by the appropriate power of 3 and you'll get your result.

#2: If , then has no solutions.