CBSE Class 10 Answered
Show that n square - 1 is divisible by 8, if n is an odd positive integer
Asked by bhakti9037 | 14 Apr, 2018, 06:59: PM
Expert Answer
If 'n' is an odd positive integer, show that (n2-1) Is divisible by 8.
Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some positive integer p.
Let n = 4p+ 1,
(n2 – 1) = (4p + 1)2 – 1 = 16p2 + 8p + 1 - 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.
Answered by Yasmeen Khan | 15 Apr, 2018, 01:20: PM
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