If n is an odd positive integer, show that `(n^2-1)` is divisible by 8.

Explanation

Let `a=n^(2) -1`
where , n is odd integer
`:'` n is an odd integer
`:.` it can be written in the form of 2m +1 for some integer m.
`"Now"" "a=n^(2) -1 =(2m+2)^(2) -1 =4m^(2) +4m +1-1 =4m(m+1)`
Now m and m+1 are consecutive integer (if one is odd then other will be even).
`:.` Exactly one of them is divisible by 2
`rArr` m(m+1) is divisible by 2
`rArr` 4m(m+1) is divisible by8
`rArr` 'a' is divisible by 8