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- W2313354182 abstract "In this paper we determine possible decompositions of Euler polynomials $E_k(x)$, i.e. possible ways of writing Euler polynomials as a functional composition of polynomials of lower degree. Using this result together with the well-known criterion of Bilu and Tichy, we prove that the Diophantine equation $$-1^k +2 ^k - cdots + (-1)^{x} x^k=g(y),$$ with $gin mathbb{Q}[X]$ of degree at least $2$ and $kgeq 7$, has only finitely many integers solutions $x, y$ unless polynomial $g$ can be decomposed in ways that we list explicitly." @default.
- W2313354182 created "2016-06-24" @default.
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- W2313354182 date "2013-01-01" @default.
- W2313354182 modified "2023-09-24" @default.
- W2313354182 title "Diophantine equations with Euler polynomials" @default.
- W2313354182 doi "https://doi.org/10.4064/aa161-3-5" @default.
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