Find 123^1001 mod 101 using the Modular Exponentiation algorithm?

Question

Find 123^1001 mod 101 using the Modular Exponentiation algorithm?

Answer 1

Fermat's little theorem is key to this problem

It tells us that, as 101 is prime, 123^ 100 = 1 mod 101

Then, (123^1001) mod 101 =

123^(100*10+1) mod 101 =

123 mod 101 =

22