Divisibility

When $10^{100}$ is divided by 7 , the remainder is...

For any natural numbers $$m, n$$, and $$k$$, such that $$k$$ divides both $$m + 2n$$ and $$3m + 4n$$, $$k$$ must be a ...

Let $$ A $$ be the largest positive integer that divides all the numbers of the form $$ 3^k + 4^k + 5^k $$, and $$ B $$...