Question

if m is an odd integer, show that m^2 - 1 is divisible by 8​

Answer 1

Hey..

{insted of m i use n.}

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Since n is odd n=4m+1 or n=4m+3.

In the first case n2−1=(n−1)(n+1)=4m⋅(4m+2)=8m(2m+1), while in the second case n2−1=(n−1)(n+1)=(4m+2)⋅(4m+4)=8(2m+1)(m+1).

So n2−1 is divisible by 8 if n is odd.