Prove that if ab is odd for integers a and b then a 3 b 3 is also odd. Use the same argument to prove that if aþb is odd then a 2 þb 2 is also odd. Prove that the product of any two even integers is a...

Prove that if ab is odd for integers a and b then a³
b³
is also odd. Use the same argument to prove that if aþb is odd then a²
þb²
is also odd.

Prove that the product of any two even integers is a multiple of 4.

Prove that for all integers n, if n is a multiple of 6 then n is also a multiple of 3.

Prove that for all integers, n, if n²
is even then n is even.

Prove the smallest proper divisor of an integer n > 1 must be prime.

Generalize by proving