I'm working on some problems where I have to find solutions in $Z_p$ and $Q_p$ of polynomials of the form $ax^2+by^2=1$. I've seen Hensel's lemma for solution over $Z_p$. For solutions over $Q_p$. I've seen the Hilbert symbol, Hasse principle and some extra theorems talking about the value of the Hilbert principle depending on $ord_p(a)$ and $ord_p(b)$. For my problems I have a list of hints and most hints talk about how I can look for a solution in $Q_p$ and how I then, because of Hensel's lemma, know that there is also a solution over $Z_p$. But I don't see why this holds?
As an example I worked of finding solutions for $x^2+17y^2=13$ in $Z_p$. I found solutions over each $Q_p$, but how do I know there are also solutions on each $Z_p$?