An approach to solving systems of polynomials via modular arithmetics with applications

The objective of this paper is twofold. First, we describe a method to solve large systems of polynomial equations using modular arithmetics. Then, we apply the approach to the study of the problem of linearizability for a quadratic system of ordinary differential equations.

► A method to solve large systems of polynomial equations using modular arithmetics is described.
► The approach is applied to the study of the problem of linearizability of ODEs.
► The linearizability conditions of the quadratic 1:−3 resonant system are obtained.