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

using Mathematical induction,prove that 3^(2n)+7 is divisible by 8.

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

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

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

Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N

Prove the following by the principle of mathematical induction: x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N.

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N

Using the principle of mathematical induction, prove that (7^(n)-3^(n)) is divisible by 4 for all n in N .