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http://dx.doi.org/10.4134/CKMS.2007.22.2.183

COMPOSITION OF BINOMIAL POLYNOMIAL  

Choi, Eun-Mi (DEPARTMENT OF MATHEMATICS HAN NAM UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.22, no.2, 2007 , pp. 183-194 More about this Journal
Abstract
For an irreducible binomial polynomial $f(x)=x^n-b{\in}K[x]$ with a field K, we ask when does the mth iteration $f_m$ is irreducible but $m+1th\;f_{m+1}$ 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;
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