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Question

If n is an odd integer then show that n21 is divisible by 8

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Solution

Any odd positive integer is in the form of 4p+1 & 4p+3 for n=4p+1
(n21)=(1p+1)21=16p2+8p+1=16p2+8p=8p(2p+1)
=(n21) is divisible by 8.
(n21)=(4p+3)21=8(2p2+3p+1)
n21 is divisible by 8
n21 is divisible by 8

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