On the reducibility of some special quadrinomials

Abstract

Let $n>m>k$ be positive integers and let $a,b,c$ be nonzero rational numbers. We consider the reducibility of some special quadrinomials $x^n+a{x}^m+b{x}^k+c$ with $n=4$ and 5, which related to the study of rational points on certain elliptic curves or hyperelliptic curves.

16 pages. Any comments are welcome!