Number theory problem

1. The problem statement, all variables and given/known data

Show that for every odd positive integer n the following is correct

xn + yn = (x+y)(xn-1 - xn-2y + xn-3y2 - ... - xyn-2 + yn-1)

2. Relevant equations

The one above.

3. The attempt at a solution

I have an idea about using induction to prove this. My idea is to write the RHS as a sum where k goes from 1 to n, and also write a similar sum where k goes from 1 to (n+2) (the next odd number). But it really have stopped there.

Since my experience with mathematical proofs is pretty nonexistent, I would appreciate any help on how to attack this problem.
 

HallsofIvy

Science Advisor
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No need to use induction, just go ahead and multiply out the right hand side.
 

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