prove: for all integers m, if m is even, then 3m + 5 is odd

prove: for any integer n, n(n^2 - 1)(n+2) is divisible by 4

prove or give a counterexample: The sum of any two irrational numbers is irrational

prove: for all integers m and n, if m mod 5 = 2 and n mod 5 = 1, then mn mod 5 = 2

prove or show a counter example: for all integers n, n^2 - n + 11 is a prime number