Commun. Korean Math. Soc. 2007 Vol. 22, No. 2, 183-194 Printed June 1, 2007

Eunmi Choi Han Nam University

Abstract : For an irreducible binomial polynomial $f(x)=x^n-b \in K[x]$ with a field $K$, we ask when does the $m$th iteration $f_m$ is irreducible but $m+1$th $f_{m+1}$ is reducible over $K$. Let $S(n,m)$ be the set of $b$'s such that $f_m$ is irreducible but $f_{m+1}$ is reducible over $K$. We investigate the set $S(n,m)$ by taking $K$ as the rational number field.