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Pythagorean Equation

Algebraic equation of the form [latex]x^{2}=y^{2}+z^{2}[/latex].
The general solution of this equation is:
  • [latex]x=k \left (m^{2} + n^{2} \right )[/latex]
  • [latex]y=k\left ( m^{2}-n^{2} \right )[/latex]
  • [latex]z=2kmn[/latex]
where k, m and n are integers.

Example

If k = 2, m = 4 and n = 3, then : x = 50, y = 14 and z = 48. Therefore : [latex]50^{2}=14^{2}+48^{2}[/latex] And : 2500 = 196 + 2304

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