Abstract

LetK be an algebraic number field of finite degree andf(X,T) a polynomial overK. For eachφ(X)∈Z[X], we denote byE(φ) the set of all integersa with φm (a) =φn (a) for somem≠n. In this paper, we give a condition for a polynomialφ(X)∈Z[X] to satisfy the following; If forn∈N, there existr∈K anda∈Z−E(φ) such thatf r, φm(a)=0, then there exists a rational functiong(X) overK andk∈N such thatf(g(T)), φk(T))=0 .

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