Q:

Remainder problem using MOD

What's the remainder when $ 43^{101} + 23^{101}$ is divided by 66?
If we use the remainder obtained when $ 43^{101} + 23^{101}$ is divided by $66$, then it becomes, 
$$13^{101}+23^{101}$$ then how can I use further MOD?

A:

Hint: $43\equiv -23\pmod{66}$. What happens when you raise $-1$ to an odd power?
Hint for a different approach. Do you know how the polynomial $x^n+y^n$ is divisible by $x+y$?

