Equation | x^2 – y^2 + x = 2*x*y

 
 
Here are the first few solutions of   x^2 - y^2 + x = 2 \, x \, y

EQ PPT 1

 
Each of the values of   x \geq 144   is the perimeter squared of the ordered primitive Pythagorean triple   (a,   a+1,   c)

EQ PPT 2

 

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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One Response to Equation | x^2 – y^2 + x = 2*x*y

  1. John McMahon says:

    y is equal to the product of the 2 consecutive Pellian numbers: c and P.

    The Hypotenuse, c = P(2n +1) and the Perimeter = P(2n + 2).

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