General question about 'vieta jumping' Suppose I want to prove that a variable posesses a certain property (e.g. is a square). For example if I wanted to prove that $x$ in $\frac{x^2+y^2+1}{xy} = k$ has the property of being a square (It is obviously false, but suppose it is true ). Is it then necessary to fix $x$ and look at the pairs $(y,k)$ (which satisfy the equation), or look at the pairs $(x,y)$ and fix k? The latter is the only version I have seen so far.

( source to the vieta jumping method : www.yimin-ge.com/doc/VietaJumping.pdf  )
In this case the problem is very simple you just need to use Vieta Jumping and find the smallest solution. In other problems that uses vieta's jumping you normally fix one varible an then you find the possible k. Here you have an example http://www.artofproblemsolving.com/community/c6h339649
In this case the problem is very simple you just need to use Vieta Jumping and find the smallest solution. In other problems that uses vieta's jumping you normally fix one varible an then you find the possible k. Here you have an example http://www.artofproblemsolving.com/community/c6h339649