I have this question but I am not sure how to proceed on it.
Find all values $a$ for which the system of the two equations $$xy=a, \quad x+y=1$$ has a solution in $\mathbb{Z}/19\mathbb{Z}$. Is there such an $a$ for which there is a unique solution?
I am not sure if the $a$ has to be in $\mathbb{Z}/19\mathbb{Z}$ or if the solutions are, so far I have $x-x^2=a$ and $y=1-x$.
Thanks for your help.