Product and sum of integer array as test for repeats

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Article #57

#57

From: Bruce Varley
Date: Sat, 21 May 2011 13:17

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This is an outcome of an industrial problem that's been solved with some 
brute force computer work, this posting is just a result of my curiosity.

We had the task of checking an array of integers for duplicates, due to the 
hardware involved the traditional approaches weren't suitable. One of our 
people came up with an algo that works for the cases that we encounter in 
the field,  I'm wondering whether the result holds for all n.

There is an array of n integers between 1 and n, with no repeated members, 
in any order. Let P be the product of all the entries, and S be the sum.

The postulate is that no other set of n integers, all between 1 and n 
(obviously containing repeats) will have the same values for both P and S.

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From: "Bruce Varley" <bv@NoSpam.com>
Newsgroups: aus.mathematics
Subject: Product and sum of integer array as test for repeats
Date: Sat, 21 May 2011 21:17:16 +0800
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