5 Proof Techniques ' 54 ' blem 5.5. n this problem, we outline a proof of the following theorem: Theorem 5.7. If n and m are nonzero integers, then n2 m2 7t 1 Your mission is to ll in the gaps and blanks, leaving no detail omitted. Proof The proOf will proceed by (insert name of proof technique or description of proof strategy here). So suppose that n2 - m2 .1 Then (n m) (n + m): 1 Since (insert relevant reason here), we conclude that both factors, (n m) and (n + m) are equal Now we cannot have n m- n + m, because (insert reason here). Therefore (insert concluding sentence) , . D Problem 5.6. Consider the two statements\" about real numbers x and y \\