# Simple Proof, Number Theory

## Homework Statement

Use direct proof to prove "The product of any two even integers is a multiple of 4."

## Homework Equations

definition of even is n=2k

## The Attempt at a Solution

My proof is going in circles/getting nowhere.

So far I have (shortened): By definition even n=2k, n=2j for some integer k
2k(2j) = 4kj = 4(kj) kj is an integer because k and j are integers
and the product of two integers is an integer
Not sure where to take it from there or if I even set the proof up correctly!

## The Attempt at a Solution

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Mark44
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## Homework Statement

Use direct proof to prove "The product of any two even integers is a multiple of 4."

## Homework Equations

definition of even is n=2k

## The Attempt at a Solution

My proof is going in circles/getting nowhere.

So far I have (shortened): By definition even n=2k, n=2j for some integer k
2k(2j) = 4kj = 4(kj) kj is an integer because k and j are integers
and the product of two integers is an integer
Not sure where to take it from there or if I even set the proof up correctly!
You have the gist of it, but you should use different letters for the two even integers, say m and n.

m = 2k, and n = 2j, for integers k an j
mk = (2k)(2j) = 4kj, which is obviously a multiple of 4.