Find the remainder when 23^23 is divided by 53?

Question

A positive integer N leaves the same remainder of 35 when divided by both 2009 and 2010.

What is the remainder when N is divided by 42?

Answer 1

The remainder is 30
The question can be reduced to [23^23 mod 53] = [a^b mod c] where a=b
23 in binary is 10111