Hey,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Small lemma about sums and products

Loading...

Similar Threads - Small lemma sums | Date |
---|---|

B Small big problem with integrals | Feb 26, 2017 |

I Problem with Theorem, Lemma and Corollary | Sep 29, 2016 |

I Does small angle mean small angular velocity? | Aug 4, 2016 |

B Small inequality | Apr 24, 2016 |

Approximation with small parameter | Jan 19, 2016 |

**Physics Forums - The Fusion of Science and Community**