Prove that if n is an odd integer, then n2 is an odd integer

Answer 1

If n is odd, it may be written as n = 2k + 1, where k is an integer.

Then, n^2 = (2k+1)^2 = 4k^2 + 4k + 1 = 2(2k+k) + 1 =

2j + 1, where j = 2(2k+k) is an integer, so n^2 is odd.