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Topic: Coprime Cubes (Read 1560 times) |
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ThudnBlunder
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Coprime Cubes
« on: Jul 4th, 2008, 6:39am » |
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Find the smallest solution to a3/b3 + c3/d3 = 6
where a,b,c,d are coprime positive integers > 100, not necessarily distinct.
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towr
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Re: Coprime Cubes
« Reply #1 on: Jul 4th, 2008, 6:58am » |
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on Jul 4th, 2008, 6:39am, ThudanBlunder wrote:| where a,b,c,d are coprime positive integers > 100, not necessarily distinct. |
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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 ?
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ThudnBlunder
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Re: Coprime Cubes
« Reply #2 on: Jul 4th, 2008, 7:21am » |
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OK, 2 of the required integers are equal. Hence consider the 3 distinct integers a,b,c to be coprime.
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Barukh
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Re: Coprime Cubes
« Reply #3 on: Jul 4th, 2008, 11:06am » |
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This is relevant.
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