Find the remainder when $1^2 + 2^2 + 3^2 + 4^2 + \cdots + 132^2$ is divided by 11.

Find the remainder when $2 + 2^2 + 2^3 + 2^4 + \cdots + 2^{100}$ is divided by 7.

When the positive integer $n$ is divided by 6 the remainder is 5. When $n$ is divided by 10, the remainder is 9. What is the remainder when $n$ is divided by 30?

Thanks so much for the Help!

I really need help on these three problems, and all of these use Mods, and Im so confused what A mod is

FBIOPENUP Oct 12, 2019