Question

Suppose a ϵ Z. Prove by contradiction that if a2 -2a + 7 is even, then a is even.

Answer 1

Your question is wrong because if $a^2-2a+7$ is even then $a$ need not to be even.

Suppose $a=1\in \Z$ . Then $a^2-2a+7=1^2-2*1+7=6$ is an even number. But $a=1$ is not even.