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        riddles >> medium >> 4 numbers product  = a perfect integer power 
        
(Message started by: gkwal on Jul 16^th, 2007, 9:33pm)

Title: 4 numbers product = a perfect integer power
Post by gkwal on Jul 16^th, 2007, 9:33pm

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

Title: Re: 4 numbers product = a perfect integer po
Post by towr on Jul 17^th, 2007, 1:45am

[hide]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 :P[/hide]