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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.)
##### Keywords:
complex polynomials; fields of characteristic zero