solution for equation For $a^2+b^2=c^2$ such that $a, b, c \in \mathbb{Z}$
Do we know whether the solution is finite or infinite for $a, b, c \in \mathbb{Z}$?
We know $a=3, b=4, c=5$ is one of the solutions.

Assuming $m,n$ be any two positive integers such that $m < n$, we have:
$$a = n^2 - m^2,\;\; b = 2mn,\;\;c = n^2 + m^2$$
And then $a^2+b^2=c^2$. 
