A university exam paper gave a short question of this type-
Find least positive integer $x$ such that $13|(x^2+1)$.
It may be an easy problem but I am clueless that without anymore conditions how to determine the value of $x$.
I understand how to apply congruence basics but here in the problem I don't know where to start and how to determine $x$.
What I think if $13$ divides $x^2+1$ then by divisibility rule, there exist a positive integer $m$ such that, $x^2+1=13.m$, which implies
Now for the consecutive positive interger values of $m$, if $x$ is not exceeding $13$, then positive interger values of $x$ are $2,3,4,....$ and so on and the least positive interger becomes $2$, when $m=1$.
I have doubt in my process. Any help is appreciated.