Diophantine equations and Bernoulli polynomials

被引：46

作者：

Bilu, YF ^{[1
]}

Brindza, B

Kirschenhofer, P

Pintér, A

Tichy, RF

Schinzel, A

机构：

[1] Univ Bordeaux 1, 351 Cours Liberat,A2X, F-33405 Talence, France

[2] Univ Debrecen, Dept Math, H-4010 Debrecen, Hungary

[3] Univ Leoben, A-8700 Leoben, Austria

[4] Graz Univ Technol, Inst Math A, A-8010 Graz, Austria

来源：

COMPOSITIO MATHEMATICA | 2002年 / 131卷 / 02期

关键词：

Diophantine equations; Bernoulli polynomials; power sums; products of consecutive integers; indecomposable polynomials;

D O I：

10.1023/A:1014972217217

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given m, n greater than or equal to 2, we prove that, for sufficiently large y, the sum 1(n) +...+ y(n) is not a product of m consecutive integers. We also prove that for m not equal n we have 1(m) +...+ x(m) not equal 1(n) +...+ y(n), provided x, y are sufficiently large. Among other auxiliary facts, we show that Bernoulli polynomials of odd index are indecomposable, and those of even index are 'almost' indecomposable, a result of independent interest.

引用

页码：173 / 188

页数：16

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