On reducible trinomials. II (Q2707266)

Let \(K\) be an algebraic number field, \(T(x;A,B)=x^n+Ax^m+B\), \(A,B\in K\), \(n>m\), \(n_1=n/(m,n),m_1=m/(n,m), n_1\geq 7\). Assume also that the trinomial \(x^{n_1}+Ax^{m_1}+B\) has a monic linear factor \(F(x)\) but no quadratic factors over \(K\). The author presents a description (Theorem 3) of all cases in which the ratio \(T(x;A,B)/F(x^{(m,n)})\) is reducible over \(K\). Similar results are also given for the case when \(K\) is a function field. NEWLINENEWLINENEWLINEFor Part I, see Diss. Math. 329, 1-83 (1993; Zbl 0795.12003), Errata in Acta Arith. 73, 399-400 (1995; Zbl 0839.12001).