Bound conditions on n- polynomials whose coefficients, roots and critical points are integers

Abstract

In this research we will provide the necessary conditions on the missing coefficients of polynomials of any degree so that roots and critical points are integers. Moreover, we completely determine all cubic polynomials whose coefficients, roots, and critical points are integers. Also the algorithm and source code to search all possible coefficients are provided.

Keywords

• critical point
• cubic polynomial
• bound condition
• n-polynomial
• monic polynomial