On the Diophantine equation 1k+2k +...+ xk = yn

被引：33

作者：

Bennett, MA ^{[1
]}

Gyory, K

Pintér, A

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

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

来源：

COMPOSITIO MATHEMATICA | 2004年 / 140卷 / 06期

关键词：

Diophantine equations; Bernoulli polynomials;

D O I：

10.1112/S0010437X04000508

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we resolve a conjecture of Schaffer on the solvability of Diophantine equations of the shape 1(k) + 2(k) +... + x(k) = y(n), for 1 less than or equal to k less than or equal to 11. Our method, which may, with a modicum of effort, be extended to higher values of k, combines a wide variety of techniques, classical and modern, in Diophantine analysis.

引用

页码：1417 / 1431

页数：15

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