Lower bounds on solutions of quadratic polynomials defined over finite rings (Q1751355)

Summary: Let \(m\) be a positive integer and let \(R_m\) denote the ring \(\mathbb{Z} /(m)\), and let \(R_m^n\) denote the Cartesian product of \(n\) copies of \(\mathbb{Z} / m\). Let \(f(\mathbf{x})\) be a quadratic polynomial in \(\mathbb{Z} [x_1, \ldots, x_n]\). In this paper, we are interested in giving lower bounds on the number of solutions of the quadratic polynomial \(f\) over the ring \(R_m^n\).