The Diophantine equation f(x) = g(y)
Yuri Bilu, Robert Tichy (2000)
Acta Arithmetica
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Displaying similar documents to “On three questions concerning -polynomials”
The Diophantine equation f(x) = g(y)
Salomon's Theorem for polynomials with several parameters
Maria Frontczak, Przemysław Skibiński, Stanisław Spodzieja (1999)
Colloquium Mathematicae
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A geometric approach to the Jacobian Conjecture in ℂ²
Ludwik M. Drużkowski (1991)
Annales Polonici Mathematici
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We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set (resp. ), then (f,g) is bijective.
On real polynomials without nonnegative roots.
Brunotte, Horst (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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On Garcia numbers.
Brunotte, Horst (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Reducibility and irreducibility of Stern -polynomials
Karl Dilcher, Larry Ericksen (2014)
Communications in Mathematics
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The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials defined by , , , and ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that can only have simple zeros, and...
Factoring polynomials over global fields
Karim Belabas, Mark van Hoeij, Jürgen Klüners, Allan Steel (2009)
Journal de Théorie des Nombres de Bordeaux
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We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field.
On the computation of the GCD of 2-D polynomials
Panagiotis Tzekis, Nicholas Karampetakis, Haralambos Terzidis (2007)
International Journal of Applied Mathematics and Computer Science
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The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.