Question

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

dear xpert, in d abov question, y do we take n = 4q +1 or 4q +3, y cant we take n = 2q+1 ??

xplain please.

Answer 1

we take 4q+1 to xplain it better as if we take n= 2q+1 n put it on place on n then we get 4q(q+1) so we have to again conclude it that q+1 is a even number while we take 4q+1 there is no need of any conclusions..