Question

Show that n^2-1 is divisible by 8 ,if n is an odd positive integer​

Answer 1

Step-by-step explanation:

If n is an odd number, then n = 4x + 1, for any number x.

n^2 - 1

= (4x + 1)^2 - 1

= 16x^2 + 1 + 8x - 1

= 16x^2 + 8x

= 8(2x^2 + x)

Clearly we can see that 8(2x^2 + x) is divisible by 8.

Hence proved that n^2-1 is divisible by 8 ,if n is an odd positive number.