Question

if n is an odd integer, then show that
n square - 1
is divisible by 8

Answer 1

let n is an odd integer and in form of 8q+1
here

the question says that n^2-1
let n= 8q+1

a= n^2-1 and a is that integer which is divisible by 8



now we can put 8q+1on the place of n (8q+1)^2-1
64q^2+16q+1-1
64q^2+16q
16q (4q+1)

and here 16q(4q+1)when divded by 8 it gives a integer and hence we can say that it is divided by 8

16q(4q+1) = 2q (4q+1) and we know that
.................. when a number divisible by
8 any number and gives
integer then that number is
divisible
hope it will help you