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Werner Mayer
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 Posted: Wed May 23, 2007 11:01 am Post subject: diophantine equation about pythagorean triples in R |
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a,b,c in R are known constants.
B,n in N are known constants.
a < b < B^n ; b < c.
(x*(B^n)+a)^2 + (y*(B^n)+b)^2 = ((x+y)*b^n+c)^2
How to find out whether solutions x \in N, y \in N do exist?
Many thanks.
Werner |
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Werner Mayer
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| Posted: Wed May 23, 2007 11:01 am Post subject: Re: diophantine equation about pythagorean triples in R |
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I produced a bad typo, using two different variables b and B.
Sorry. I will rephrase the problem:
a,b,c in R are known constants.
k, n in N are known constants.
a < b < k^n ; b < c.
(x*(k^n)+a)^2 + (y*(k^n)+b)^2 = ((x+y)*(k^n)+c)^2
How to find out whether solutions x \in N, y \in N do exist?
Many thanks.
Werner |
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Ulrich Diez
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| Posted: Fri May 25, 2007 11:01 am Post subject: Re: diophantine equation about pythagorean triples in R |
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Werner Mayer wrote:
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a,b,c in R are known constants.
k, n in N are known constants.
a < b < k^n ; b < c.
(x*(k^n)+a)^2 + (y*(k^n)+b)^2 = ((x+y)*(k^n)+c)^2
How to find out whether solutions x \in N, y \in N do exist?
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rotfl. I don't think you will get an easy answer.
For special cases of a, b and c your equation resolves to factoring
integers... Why do you need this? Can you tell more about
a,b and c?
Ulrich |
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