# Math Help - MATH question - induction!?

1. ## MATH question - induction!?

Let a,b be two positive natural numbers. Prove that for every positive odd number n, a^n + b^n is divided by a+b

2. Originally Posted by tukilala
Let a,b be two positive natural numbers. Prove that for every positive odd number n, a^n + b^n is divided by a+b
Hint: Prove that $a^n + b^n = (a+b)\left( \sum_{k=0}^{n-1} (-1)^k a^{k-n} b^k \right)$

3. Originally Posted by ThePerfectHacker
Hint: Prove that $a^n + b^n = (a+b)\left( \sum_{k=0}^{n-1} (-1)^k a^{k-n} b^k \right)$
Here is the expanded notation [n is a positive odd integer]:

$a^n + b^n = (a + b)(a^{n-1} - a^{n-2}b + a^{n-3}b^2 - \cdots + a^2b^{n-3} - ab^{n-2} + b^{n-1})$