Show that `a^(n) - b^(n)` is divisible by `a – b` if n is any positive integer odd or even.

Show that a^(n) - b^(n) is divisible by (a + b) when n is an even positive integer. but not if n is odd.

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

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

Using binomial theorem show that 3^(4n+1)+16n-3 is divisible by 256 if n is a positive integer.

n(n^(2)-1), is divisible by 24 if n is an odd positive number.

Prove,by mathematical induction,that x^(n)+y^(n) is divisible by x+y for any positive odd integer n.

Prove that n^(2)-n divisible by 2 for every positive integer n.

Show that one and only one out of n , n +1 and n +2 is divisible by 3 , where n is any positive integer.

Show that one and only one out of n, n + 2, n + 4 is divisible by 3, where n is any positive integer.