Problem on pythagorean triples There are $200$ balls in a pot numbered from $1$ to $200$.A ball is choosen at random.

What is the probability that Ball No. is a member of pythagorean triples?
Also find out the pythagorean triples.

Suppose I choose $31$,then how I find any two number $a,b$,so that,$31$ is member of pythagorean triples?
Is it manual or have some methods?

Notice 
$$\begin{align}(2k)^2 + (k^2-1)^2 &= (k^2+1)^2\\
(2k+1)^2 + (2k(k+1))^2 &= (2k^2+2k+1)^2
\end{align}$$
every integer $n \ge 3$ is part of a Pythragorean triple.
For the case $n = 31$, substitute $k = 15$ into $2^{nd}$ identity and you get
$31^2 + 480^2 = 481^2$.
