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Topic: 4 numbers product = a perfect integer power (Read 213 times) |
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gkwal
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4 numbers product = a perfect integer power
« on: Jul 16th, 2007, 9:33pm » |
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given 81 integers all of whose prime factors are from { 2 3 5}, there are 4 numbers whose product is a perfect integer power 4
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towr
wu::riddles Moderator
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Re: 4 numbers product = a perfect integer po
« Reply #1 on: Jul 17th, 2007, 1:45am » |
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You can represent the integers by the number of times each factor occurs. Then take these numbers modulo 4.
If there are four that are equal, taking them together works. The other cases are more tedious, and I'm short on time 
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Wikipedia, Google, Mathworld, Integer sequence DB
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