On the relationship between the number of solutions of congruence systems and the resultant of two polynomials

Dmitry I. Khomovsky

Let $q$ be an odd prime and $f(x)$, $g(x)$ be polynomials with integer coefficients. If the system of congruences $f(x)\equiv g(x)\equiv 0(\mathrm{mod}q)$ has $\ell$ solutions, then $R…