Let x be an integer. If x is odd, then x^2 is odd

Let x be an integer. If x is odd, then x^2 is odd

Proof: Let x be an odd number. This means that x = 2n + 1 where n is an integer.

Squaring x, we get:
x^2 = (2n + 1)^2 = (2n + 1)(2n + 1)
x^2 = 4n^2 + 4n + 1
x^2 = 2(2n^2 + 2n) + 1

2(2n^2 + 2n) is an even number since 2 multiplied by any integer is even
So adding 1 is an odd number