We can prove this statement using proof by contrapositive.
First, we will assume the contrapositive statement: If a is even, then a^2-2a+7 is odd.
Suppose a is even. Then we can write a as a = 2k for some integer k.
Substituting this into the expression a^2-2a+7, we get:
a^2 - 2a + 7 = (2k)^2 - 2(2k) + 7
= 4k^2 - 4k + 7
= 2(2k^2 - 2k + 3) + 1
Since 2k^2 - 2k + 3 is also an integer, we have expressed a^2-2a+7 as an odd integer plus one. Therefore, a^2-2a+7 is odd.
This completes the proof of the contrapositive statement.
Since the contrapositive is true, the original statement must also be true. Therefore, if a^2-2a+7 is even, then a is odd.
Prove if a^2-2a+7 is even, then a is odd?
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