Hello all

Diophantine Pythagorean theorem.

Prove this Conjecture:

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) positive integers.

k=((p-2)*p-1)/2

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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