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

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a2 -2a + 7 for a ϵ Z is odd sense a*2 -2*a +7 = 7

If the task condition a2-2*a+7:

a2-2*a+7 = (a-2)2+3

(a-2)2+3 is even if (a-2)2 is odd

if (a-2)2 is odd then a is odd

Hence the hypothesis is false and proof is not possible

Answer: proof is not possible

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