Diophantine equations with Euler polynomials

Dijana Kreso, and Csaba Rakaczki. "Diophantine equations with Euler polynomials." Acta Arithmetica 161.3 (2013): 267-281. <http://eudml.org/doc/279149>.

@article{DijanaKreso2013,
abstract = {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.},
author = {Dijana Kreso, Csaba Rakaczki},
journal = {Acta Arithmetica},
keywords = {Euler polynomials; decomposition; higher degree equations},
language = {eng},
number = {3},
pages = {267-281},
title = {Diophantine equations with Euler polynomials},
url = {http://eudml.org/doc/279149},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Dijana Kreso
AU - Csaba Rakaczki
TI - Diophantine equations with Euler polynomials
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 3
SP - 267
EP - 281
AB - 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.
LA - eng
KW - Euler polynomials; decomposition; higher degree equations
UR - http://eudml.org/doc/279149
ER -