Composition of Binomial Polynomial
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.
Keywords : iterated polynomial, Diophantine equation, ABC conjecture
MSC numbers : 12E05, 11D41
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