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Integer coordinate set of points that is a member of sphere surface

Assume $C$ is a sphere with radius $r$ and center in the origin (0,0,0). How can we find the set of all points with integer coordinates that lie on the surface of $C$?

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Khaled
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  • Related: http://en.wikipedia.org/wiki/Gauss_circle_problem – Bill Cook Sep 02 '12 at 20:16
  • @BillCook That gives points inside a circle, I require points on a surface. – Khaled Sep 02 '12 at 20:29
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    Related: http://math.stackexchange.com/questions/76892/pythagorean-quadruples –  Sep 02 '12 at 20:34
  • Is the radius an integer, or the square root of an integer? – Lubin Sep 02 '12 at 20:34
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    @Lubin: if it's not the square root of an integer, the answer is easy. – Robert Israel Sep 02 '12 at 20:44
  • @Lubin Not necessarily, but it depends on what values of $r$ can generate solutions. – Khaled Sep 02 '12 at 20:56
  • @GerryMyerson Yet that question has no answer either. – Khaled Sep 03 '12 at 06:37
  • Well, it does, just not an efficient answer. There is also a suggestion that this is a Project Euler problem, and we don't do those here. – Gerry Myerson Sep 03 '12 at 07:12
  • @GerryMyerson No this subject was discussed in my number theory class. I would also kindly request you stop accusing me of posting PE problems on every question I post. – Khaled Sep 03 '12 at 08:11
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    "I would also kindly request you stop accusing me of posting PE problems on every question I post." Khaled, you have posted 12 questions. On 10 of them I have made no mention whatever of Project Euler. Please refrain from telling lies about my activity here. – Gerry Myerson Sep 03 '12 at 13:04

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