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25093Diophantine equation

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  • Sebastian Martin Ruiz
    May 24, 2013
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      Hello all:

      Let c an even positive integer number fixed.


      Consider the quadratic equation in two variables:


      -3x^2+y^2-2xy-4cx+4cy+4=0

      Can anyone prove that for every c large enough there is at least one other than the trivial solution (1,1)  of the equation with x and y both positive integers? i.e. (y>x>1 integers)


      Sincerely

      Sebastián Martín Ruiz

      P.S. (It is related to the prime numbers. I'll tell you soon.)


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