# 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