Reducibility of polynomials of the form f(x)-g(y)
A. Schinzel (1967)
Colloquium Mathematicae
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A. Schinzel (1967)
Colloquium Mathematicae
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Andrzej Schinzel (1995)
Banach Center Publications
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Karl Dilcher, Rob Noble, Chris Smyth (2011)
Acta Arithmetica
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Thomas Ernst (2016)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In the first article on q-analogues of two Appell polynomials, the generalized Apostol-Bernoulli and Apostol-Euler polynomials, focus was on generalizations, symmetries, and complementary argument theorems. In this second article, we focus on a recent paper by Luo, and one paper on power sums by Wang and Wang. Most of the proofs are made by using generating functions, and the (multiple) q-addition plays a fundamental role. The introduction of the q-rational numbers in formulas with...
Souad El Otmani, Armand Maul, Georges Rhin, Jean-Marc Sac-Épée (2013)
Journal de Théorie des Nombres de Bordeaux
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In this work, we propose a new method to find monic irreducible polynomials with integer coefficients, only real roots, and span less than 4. The main idea is to reduce the search of such polynomials to the solution of Integer Linear Programming problems. In this frame, the coefficients of the polynomials we are looking for are the integer unknowns. We give inequality constraints specified by the properties that the polynomials should have, such as the typical distribution of their roots....
Amdeberhan, Tewodros (2010)
Integers
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Yann Bugeaud, Andrej Dujella (2014)
Acta Arithmetica
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We construct parametric families of (monic) reducible polynomials having two roots very close to each other.
L. Hajdu, R. Tijdeman (2003)
Acta Arithmetica
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Djordjević, Gospava B. (1997)
Matematichki Vesnik
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D. Markovitch (1951)
Matematički Vesnik
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Thomas Ernst (2015)
Annales UMCS, Mathematica
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We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...
Thomas Ernst (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol–Bernoulli and Apostol–Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...