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

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

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

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

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

3^(2n)+24n-1 is divisible by 32 .

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.

3^(2n)+24n-1 is divisible;

By the principle of mathematical induction prove that (5^(2n)-1) is always divisible by 24 for all positive integral values of n.

The expression 31^(n) + 17^(n) is divisible by, for every odd positive integer n :