find the remainder when 7^99 is divided by 101

Euler of 101 = 100

So, 7^100 mod 101 = 1
7 * 7^99 mod 101 = 1
Let 7^99 mod 101 = k
=> 7k mod 101 = 1

=> 7k = 101p + 1
p = 2 satisfies for k = 29
So, remaninder = 29