Prove or give counter examples for the following problems
1) For any integer n, (n^2 + 2n)mod4 is equal to 0 or 3.
2) Suppose m, n, and d are integers, and m mod d = n mod d. Prove that dl(m - n) (says d divides (m minus n).
3) If n^3 is odd, then n is odd
4) If a, b, and c ate integers and a^2 + b^2 = c^2, then at least one of a, b, and c is odd
5) Prove that the cube root of 4 is irrational