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## Diophantine Pythagorean theorem CORRECT

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• Hello all Diophantine Pythagorean theorem.   Prove this Theorem:   “ If p is a ODD prime number then the following Diophantic Equation   p^2+(p+k)^2=q^2
Message 1 of 1 , Aug 25, 2008
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Hello all

Diophantine Pythagorean theorem.

Prove this Theorem:

 If p is a ODD 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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