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