Question

For what values of,n²-1 is divisible by 8.

Answer 1

The values of n would be:
=> 3^2-1 = 8 which is divisible by 8. Then,
=> 5^2-1 = 24 which is divisible by 8.


Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p.

Let n = 4p+ 1,

(n2 – 1) = (4p + 1)2 – 1 = 16p2 + 8p + 1 = 16p2 + 8p = 8p (2p + 1)
⇒ (n2 – 1) is divisible by 8.

(n2 – 1) = (4p + 3)2 – 1 = 16p2 + 24p + 9 – 1 = 16p2+ 24p + 8 = 8(2p2 + 3p + 1)
⇒ n2– 1 is divisible by 8.

Therefore, n2– 1 is divisible by 8 if n is an odd positive integer