7.Show that n2- 1 is divisible by 8, if n is an odd positive integer. – InterviewSolution

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1.	7.Show that n2- 1 is divisible by 8, if n is an odd positive integer.
Answer» Sol:Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p.Let n = 4p+ 1,(n2– 1) = (4p + 1)2– 1 = 16p2+ 8p + 1 = 16p2+ 8p = 8p (2p + 1)⇒ (n2– 1) is divisible by 8.(n2– 1) = (4p + 3)2– 1 = 16p2+ 24p + 9 – 1 = 16p2+ 24p + 8 = 8(2p2+ 3p + 1)⇒ n2– 1 is divisible by 8.Therefore, n2– 1 is divisible by 8 if n is an odd positive integer.

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