How can we conclude that the given number will come in a pythagorean triplet? How can we conclude that the given number can form a pythagorean triplate or not? Can we find that triplet? For example the given number is 3. 3,4,5 is a pythagorean triplate which includes 3. So our answer for the number three is 3,4,5 & triplet is possible.

Any odd number $2n+1$ is part of the triplet $2n+1,2n^2+2n,2n^2+2n+1$. If $m$ is even, and not a power of 2, then $m=2^k(2n+1)$ for some $k$ and $n$, and $m$ is a part of $m,2^k(2n^2+2n),2^k(2n^2+2n+1)$. And if $n$ is a power of $2$, then it's part of $3s,4s,5s$ for appropriate $s$. The only exceptions are $n=1$ and $n=2$.