
 Diophantine Equations (Site not responding. Last check: 20071106) 
  In general, the above "algebraic equations in the domain of integer numbers" can be defined as P=0, where P is a polynomial with integer coefficients and one, two or more variables (the "unknowns"). 
  The equation (1) always represents in the (x, y)plane a curve(an ellipse, a hyperbola, or a parabola), one or two straight lines, one isolated point, or nothing. 
  Since D and a are not 0, this means that a solution (X, Y) of the reduced equation (2) yields a solution (x, y) of the equation(1), iff Xbd+2ae is divisible by D and Ybyd is divisible by 2a(else x and y would not be integer numbers). 
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