Appendix - Mathematical Induction and Other Forms of Proofs - Exercises - Page A6: 13

See below.

Assume the statement is false. Then there exists an even $p=2n$ (where $n$ is an integer), such that $p^2$ is odd. But $p^2=4n^2$ and the $4$ in the product definitely makes $p^2$ even. Thus the statement is true.