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

被引：0

作者：

Györy, K ^{[1
]}

Pintér, A ^{[1
]}

机构：

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

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2003年 / 62卷 / 3-4期

关键词：

Superelliptic equations; Bernoulli polynomials;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In our paper a survey is given on the title equation. General finiteness theorems, bounds on n and the number of solutions, complete solution for small values of k, and some generalizations and analogues are presented. The basic ideas of the most important proofs are also outlined. We note that in the proofs of the recent results virtually every technique of modern Diophantine analysis has been employed.

引用

页码：403 / 414

页数：12

共 6 条

[1] On the Diophantine equation 1k+2k +...+ xk = yn
Bennett, MA
Gyory, K
Pintér, A
COMPOSITIO MATHEMATICA, 2004, 140 (06) : 1417 - 1431
[2] On some generalizations of the diophantine equation s(1k+2k + ... + xk) + r = dyn
Rakaczki, Csaba
ACTA ARITHMETICA, 2012, 151 (02) : 201 - 216
[3] On the Diophantine equation (x+1)k (x+2)k + . . . plus (lx)k = yn
Soydan, Gokhan
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2017, 91 (3-4): : 369 - 382
[4] The Diophantine equation (x+1)k + (x+2)k + ... plus (lx)k = yn revisted
Bartoli, Daniele
Soydan, Gokhan
PUBLICATIONES MATHEMATICAE DEBRECEN, 2020, 96 (1-2): : 111 - 120
[5] On the number of solutions of the equation 1k+2k+•••+(x-1)k=yz
Brindza, B
Pintér, A
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2000, 56 (3-4): : 271 - 277
[6] A few remarks on the values of the Bernoulli polynomials at rational arguments and some relations with ζ(2k
de Camargo, Andre Pierro
de Oliveira Teruya, Giulliano Cogui
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2021, 27 (04) : 180 - 186

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