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19547Diophantine Pythagorean theorem

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  • Sebastian Martin
    Aug 25, 2008
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      Diophantine Pythagorean theorem.
       
      Prove this Theorem:
       
      “ If p is a prime number then the following Diophantic Equation
       
      p^2+(p+k)^2=q^2
       
      has only one solution. (p, k ,q) integers.
       
      k=((p-2)*p-1)
       
      q=(p^2+1)/2  “
       
       
       
       
      Countraexample for the composite case:
       
      p=9       9^2 +(9+3)^2=15^2           (9,3,15)
       
                    9^2+(9+31)^2=41^2         (9,31,41)
      Sebastián Martin Ruiz

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