New posts in Vieta Jumping

What are all possible positive integers $k$ such that $k=\frac{a^2+b^2+c^2}{bc+ca+ab}$ for some positive integers $a$, $b$, and $c$?

A generalization of the (in)famous IMO 1988 problem 6: If $\frac{a^2 + b^2 - abc}{ab + 1}$ is a positive integer then it is a square.

Show that infinitely many positive integer pairs $(m,n)$ exist s.t $\frac{m+1}{n}+\frac{n+1}{m} \in \mathbb{N}$

Showing that $m^2-n^2+1$ is a square

Is it true that $f(x,y)=\frac{x^2+y^2}{xy-t}$ has only finitely many distinct positive integer values with $x$, $y$ positive integers?

Divisibility - Math Olympiad: $x|(y^2+m)$ and $y|(x^2+m) $

Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer

Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.