Lower Bounds on Solutions of Quadratic Polynomials Defined over Finite Rings

Abstract EN

Let m be a positive integer and let Rm denote the ring Z/(m), and let Rmn denote the Cartesian product of n copies of Z/m.

Let f(x) be a quadratic polynomial in Z[x1,…,xn].

In this paper, we are interested in giving lower bounds on the number of solutions of the quadratic polynomial f over the ring Rmn.