- #1

- 7

- 0

I'm trying to prove a larger theorem; in order to complete my proof I need to use the following lemma (or, if it turns out to be false, try a completely different method of proof):

Consider any two sets of n nonzero integers, A and B. If their respective sums and products are equal, then A = B.

i.e if A = {a1, a2, ... aN} and B = (b1, b2, ... bN},

and a1*a2*...*aN = b1*b2*...*bN

and a1 + a2 +... + aN = b1 + b2 + ... bN

then A and B are the same set.

For some reason I'm sure I've seen this theorem before, but I can't for the life of me remember where or whether it was exactly this or slightly different. I'd search it on Google, but then I'd need to know what terms to search for - and if I knew that I would probably know the answer.

So, any ideas/pointers/links to wikipedia articles are very much appreciated.