A student is asked to prove that if $n$ and $m$ are odd integers, then $n^2+m^2$ is even.

Explain why the following argument is VALID or INVALID:

Proof:

Since $n$ and $m$ are odd integers, let $n=7$ and $m=9.n=7$ is odd because $7=2*3+1,$ and $m=9$ is odd because $9=2*4+1.$ Substituting into the expression $n^2+m^2$ yields $n^2+m^2=7^2+9^2=130=2*65.$ Therefore, by definition $n^2+m^2$ is even.