Question

if n is an odd integer, then show that n^2-1 is divisible by 8
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Answer 1

Use the general form of an odd number =2x+1, where x=0,1,2....

Thus n^2-1= (2x+1)^2-1=4x^2+4x+1-1

=4x^2+4x.

Thus it is divisible by 8