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On \(f^3(t)-g^2(t)\). (English) Zbl 0136.25204
Answering a question of B. J. Birch, S. Chowla, M. Hall jun. and A. Schinzel [Norske Vid. Selsk. Forhdl. 38, 65–69 (1965; Zbl 0144.03901)] the author proves that if \(f(t), g(t)\) are polynomials with arbitrary complex coefficients then \(\deg(f^3-g^2)\geq \deg f+1\), except when \(f^3=g^2\), identically. This result is generalized to the case of \(af^l-bg^m\), where \(a,b,f,g\) are polynomials over any field of characteristic 0.
Reviewer: A. Schinzel

MSC:
12D05 Polynomials in real and complex fields: factorization
12E05 Polynomials in general fields (irreducibility, etc.)
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