Question

show that n2-1 is divisible by 8 if n is an odd positive integer

Answer 1

Any odd positive integer is of the form (2k - 1) Hence substituting 2k - 1 in place of n in the given expression ( n^2 - 1 )

= (2k - 1)^2 - 1

= 4k^2 - 4k + 1 - 1

= 4( k^2 - k)

Hence n^2 - 1 is always divisible by 4 and therefore it is also Always divisible by 8 as 8 is a multiple of 4!

Hope you understood!