Question: . (4 marks) Complete the following proof that The sum of two perfect sqares is even. 0 Let a, b E Z. Then (12,52 6

. (4 marks) Complete the following proof that \"The sum of two perfect sqares is even.\" 0 Let a, b E Z. Then (12,52 6 N are perfect squares. 0 Case 1: a,b are both even. 0 Then, a : 2n and b : 2m for some n, m E Z. So, a2 : 2(2n2) b2 : 2(2m2) 0 Consider a2 + b2 = 2(2n2) + 2(2m2) = 2 (2712 + 2mg) 0 Since 2,n,m E Z let j = 2712 + 2m2 6 Z. Therefore, a2 + b2 = 23' for some j E Z, so the sum of two perfect squares is even. 0 Case 2: a is even, and b is odd, without loss of generality 0 (Fill in the blanks) Then, a : b 2 0 (Fill in the blank) So, a2 : b2 : 0 Consider a2 + [)2 0 (Finish the proof of this case) 0 (Answer this question:) What case is missing

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