# I Proving Odd and Even

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1. Feb 13, 2016

### bronx

How to do this type of problem. I am confused, right now.
Prove that x-y is even and x2-xy+3 is odd

2. Feb 13, 2016

### Staff: Mentor

$7-2=5$ is not even and $7^2 - 7*2 + 3 =38$ is not odd.
However, if $x-y$ is even, then $x^2 - xy + 3 = x(x-y)+3$ is odd.
Proof: If $2|(x-y)$ then $2|x(x-y)$ and dividing $x^2 - xy + 3 = x(x-y)+3$ by $2$ has a remainder $1$.

3. Feb 18, 2016