I have an exercise sheet without solutions, and I'm stuck on the last question. We consider the following diophantine equations :
$(E11)\quad :\quad x^2-5y^2=11$
and
$(E6)\quad :\quad x^2-5y^2=6$
Both equations have a solution in $\mathbb Z_5$ (they are in fact equivalent in $\mathbb Z_5$). $(E11)$ has one in $\mathbb Z$, with $x=4$ and $y=1$. $(E6)$ has no solution in $\mathbb Z$ as it can be shown not to have any in $\mathbb Z_4$.
The question is : "Conclude from a theorem about solutions of diophantine equations in $\mathbb Z$ and $\mathbb Z_n$".
I can't find a theorem that seems helpful here, and I can't even see what I might want to conclude from this ? Does it point out anything worth noticing ?