Geodesic
Diophantine equations with Euler polynomials
Dijana Kreso 1   ; Csaba Rakaczki 2
1 Institut für Analysis und Computational Number Theory (Math A) Technische Universität Graz Steyrergasse 30/II 8010 Graz, Austria
2 Institute of Mathematics University of Miskolc H-3515 Miskolc Campus, Hungary
Acta Arithmetica, Tome 161 (2013) no. 3, pp. 267-281 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We determine decomposition properties of Euler polynomials and using a strong result relating polynomial decomposition and diophantine equations in two separated variables, we characterize those $g(x)\in \mathbb {Q}[x]$ for which the diophantine equation $$-1^k +2 ^k - \cdots + (-1)^{x} x^k=g(y) \hskip 1em\ {\rm with}\ k\geq 7$$ may have infinitely many integer solutions. Apart from the exceptional cases we list explicitly, the equation has only finitely many integer solutions.
DOI : 10.4064/aa161-3-5
Keywords: determine decomposition properties euler polynomials using strong result relating polynomial decomposition diophantine equations separated variables characterize those mathbb which diophantine equation cdots y hskip geq may have infinitely many integer solutions apart exceptional cases list explicitly equation has only finitely many integer solutions

Dijana Kreso  1   ; Csaba Rakaczki  2

1 Institut für Analysis und Computational Number Theory (Math A) Technische Universität Graz Steyrergasse 30/II 8010 Graz, Austria
2 Institute of Mathematics University of Miskolc H-3515 Miskolc Campus, Hungary 
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Dijana Kreso; Csaba Rakaczki. Diophantine equations with Euler polynomials. Acta Arithmetica, Tome 161 (2013) no. 3, pp. 267-281. doi: 10.4064/aa161-3-5

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