Can x-y Be Even While x²-xy+3 Is Odd?

[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

 

[fresh_42]

$7-2=5$ 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 $1$.

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Thread will remain closed. Just a reminder, when you see misplaced schoolwork/homework type questions in the general math forums (especially when the OP shows zero effort to solve the problem), please Report the post rather than responding. Thanks.