If a mod would like to move this to it's assigned section please do so, I don't know which one it belongs into.

sorry i'm not good with latex

Q1. Prove the following biconditional statement

1. For any a in Z(set of integers) a not logically equivalent to 0(mod 3) if and only if a^2 is logically equivalent with 1(mod 3)

2.Prove that if a is an odd integer, then for any x in Z(set of integers), x^2 - x - a does not equal 0

3. Use mathematical induction to prove that for any natural number n, 3 divides (2^(2n) - 1 ). Specify each step in the process clearly.

Thank you soo much (: