Question

If n ia an odd integer then show that n2 - 1 is divisible by 8

Answer 1

HEY HERE IS UR ANSWER

We know that odd positive integer is in the form of 4q+1 4q+3

Now when n=4q+1 then
n2-1 = (4q+1)2-1=16q2+8q+1-1= 8(2q2+1)
n2-1=8m where m=2q2+1
Therefore n2-1 is divisible by 8

Now when n=4q+3 then
n2-1= (4q+3)2-1=16q2+24q+9-1=16q2+24q+8=8(2q2+3q+1)=8m where m=2q2+3q+1
Therefore n2-1 is divisible by 8

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