Pythagorean Equation

Pythagorean Equation

Algebraic equation of the form \(x^{2}=y^{2}+z^{2}\).


The general solution of this equation is:

  • \(x=k \left (m^{2} + n^{2} \right )\)
  • \(y=k\left ( m^{2}-n^{2} \right )\)
  • \(z=2kmn\)

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 : \(50^{2}=14^{2}+48^{2}\)

And : 2500 = 196 + 2304

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