Prove the sum of two odd numbers is even | MathCelebrity Forum

Prove the sum of two odd numbers is even

math_celebrity

Staff member
Take two arbitrary integers, x and y

We can express the odd integer x as 2a + 1 for some integer a
We can express the odd integer y as 2b + 1 for some integer b

x + y = 2a + 1 + 2b + 1
x + y = 2a + 2b + 2

Factor out a 2:
x + y = 2(a + b + 1)

Since 2 times any integer even or odd is always even, then x + y by definition is even.

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