COMPOSITION OF BINOMIAL POLYNOMIAL

Abstract

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