On the number of terms in the irreducible factors of a rational polynomial

Abstract

For an integer $m \geq 3$, does there exist an absolute constant $K(m)$ such that every polynomial with $m$ non-zero coefficients has an irreducible factor with at most $K(m)$ coefficients? A previous result in the literature establishes $K(3) \geq 9$, which is here improved to $K(3) \geq 12$. Improvements on known bounds are also given for $m=4,5,6$, and for $K(m)$, when $m \geq 7$.