- #1

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## Homework Statement

Prove that the product of two even integers is divisible by four.

## Homework Equations

## The Attempt at a Solution

If a·b where (a^b)ЄZ

^{+}, then 4|(a·b)

If 2|a ^ 2|b, then (a^b)≥2 v (a·b)=0

If 2|(2·n) then 4|[2·(2·n)] for nЄZ

∴ 4|(a·b) where (a^b)ЄZ

^{+}

[X]

Is my proof correct? Is my notation for a positive integer correct (Z

^{+}), or should I not use the

^{+}and instead state that a,b≥0 a,bЄK? I'm not sure if that really proves it or not, but it's the best I have at the moment.

I was given much shorter proofs after I constructed this, and am aware it can be much shorter, but I mainly want to know if this is CORRECT or not.

Thank you!