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riddles >> hard >> Coprime Cubes
(Message started by: ThudanBlunder on Jul 4th, 2008, 6:39am)

Title: Coprime Cubes
Post by ThudanBlunder on Jul 4th, 2008, 6:39am
Find the smallest solution to a3/b3 + c3/d3 = 6
where a,b,c,d are coprime positive integers > 100, not necessarily distinct.

Title: Re: Coprime Cubes
Post by towr on Jul 4th, 2008, 6:58am

on 07/04/08 at 06:39:31, ThudanBlunder wrote:
where a,b,c,d are coprime positive integers > 100, not necessarily distinct.
If they're coprime, and >100, then I'd say they're necessarily distinct.
Or do you mean something other than pairwise coprime? i.e. gcd(a,b)=gcd(a,c)=gcd(a,d)=gcd(b,c)=gcd(b,d)=gcd(c,d)=1 ?

Title: Re: Coprime Cubes
Post by ThudanBlunder on Jul 4th, 2008, 7:21am
OK, 2 of the required integers are equal. Hence consider the 3 distinct integers a,b,c to be coprime.

Title: Re: Coprime Cubes
Post by Barukh on Jul 4th, 2008, 11:06am
This (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1183726039) is relevant.



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