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

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

(1+x)^n-nx-1 is divisible by (where n in N)

Prove by induction method that n(n^(2)-1) is divisible by 24 when n is an odd positive integer.

Prove the following by the method of mathematical induction. : n^3+(n+1)^3+(n+2)^3 is divisible by 9, when n is a positive integer.

By principle of mathematical induction show that a^(n)-b^(n) is divisible by a+b when n is a positive even integer.

Show that by mathematical induction, 3.5^(2n+1) + 2^(3n+1) is divisible by 17, when n > =0 is an integer.

By induction method prove that, (a^(n)+b^(n)) is divisible by (a+b) when n is an odd positive integer .

Prove that (x - y) can never be a factor of the polynomial x^(n)+y^(n) , where n is any positive integer (odd or even).

Prove that by mathematical induction : 3^(2n+ 2) - 8n - 9 is divisible by 64 where n in N.

Show that for any positive integer 3^(2n+2)-8n-9 is divisible by 64 .