
# 5.2: Non-Linear Diophantine Equations


The following are some examples of non-linear Diophantine equations:

## Pythagorean Equation

Equations of the form $$x^2+y^2=z^2$$, where $$x,y,z \in \mathbb{Z}$$.

## Pell's Equation

Equations of the form $$x^2-2y^2=1$$, where $$x,y,z \in \mathbb{Z}$$. The solutions give rise to square triangular numbers.