Diophantine equations with Euler polynomials

• Autorzy: Dijana Kreso , Csaba Rakaczki
• Języki publikacji: EN

Abstrakty

EN

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) ∈ ℚ [x] for which the diophantine equation
$-1^k + 2^k - ⋯ + (-1)^{x} x^k = g(y)$ with k ≥ 7
may have infinitely many integer solutions. Apart from the exceptional cases we list explicitly, the equation has only finitely many integer solutions.

Kategorie tematyczne

• 11D41: Higher degree equations; Fermat's equation
• 11B68: Bernoulli and Euler numbers and polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 3
• Strony: 267-281

Daty

wydano

2013

Twórcy

autor

Dijana Kreso

• Institut für Analysis und, Computational Number Theory (Math A), Technische Universität Graz, Steyrergasse 30/II, 8010 Graz, Austria

autor

Csaba Rakaczki

• Institute of Mathematics, University of Miskolc, H-3515 Miskolc Campus, Hungary

Identyfikatory

DOI

10.4064/aa161-3-5