The following definitions will be used in the proof of the statement.

An integer n is even if, and only if, n equals twice some integer. An integer n is odd if, and only if, n equals twice some integer plus 1. Symbolically, for any integer, n
n is even ⇔ n = 2k for some integer k
n is odd ⇔ n = 2k + 1 for some integer k
Prove the following statement.
The difference of any two odd integers is even.

step-by-step explanation:

compare

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus