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.
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页码：1417 / 1431
页数：15
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