On the equation φ(Xm-1) = Xn-1

被引：3

作者：

Faye, Bernadette ^{[1
,2
]}

Luca, Florian ^{[2
]}

机构：

[1] Univ Cheikh Anta Diop Dakar, Ecole Doctorale Math & Informat, Dakar, Senegal

[2] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2015年 / 11卷 / 05期

关键词：

Diophantine equations; applications of primitive divisors of Lucas sequences; applications of sieve methods;

D O I：

10.1142/S1793042115400187

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here, we show that the title equation has only finitely many positive integer solutions (X, m, n), where phi is the Euler function.

引用

页码：1691 / 1700

页数：10

共 50 条

[31] On the Diophantine equations of the form λ1Un1 + λ2Un2 + ••• plus λkUnk = wp1z1 p2z2 ••• pszs
Goedhart, Eva
Ha, Brian
McBeath, Lily
Velasco, Luisa
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2024, 30 (03):
[32] On the Diophantine equations (x-1)3 + x5 + (x+1)3 = yn and (x-1)5 + x3 + (x+1)5 = yn
Zhang, Zhongfeng
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2017, 91 (3-4): : 383 - 390
[33] The Egyptian fraction of the form 1/a
Prugsapitak, Supawadee
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2023, 18 (04) : 595 - 597
[34] On the Diophantine equations (x -1)3 + x5 + (x + 1)3 = yn and (x - 1)5 + x3 + (x + 1)5 = yn (vol 91, pg 383, 2017)
Zhang, Zhongfeng
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2018, 93 (1-2): : 261 - 262
[35] A note on the simultaneous Pell equations x2-(a2-1)y2=1 and y2-bz2=1
Jiang, Xing-Wang
PERIODICA MATHEMATICA HUNGARICA, 2020, 81 (02) : 234 - 238
[36] SOLVING DIOPHANTINE EQUATIONS (an- 1)(b(m)-1) = x(2) BY USING PELL'S EQUATIONS
Jaidee, S.
Wannalookkhee, F.
Janthawee, M.
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2018, 40 (02): : 147 - 151
[37] DIVISIBILITY PROPERTIES OF INTEGERS-X,K SATISFYING 1(K)+...+(X-1)(K)=X(K)
MOREE, P
TERIELE, HJJ
URBANOWICZ, J
MATHEMATICS OF COMPUTATION, 1994, 63 (208) : 799 - 815
[38] On distinct unit fractions whose sum equals 1
Burshtein, N
DISCRETE MATHEMATICS, 2005, 300 (1-3) : 213 - 217
[39] On the decoding of 1-Fibonacci error correcting codes
Bellini, Emanuele
Marcolla, Chiara
Murru, Nadir
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2021, 13 (05)
[40] Complete solutions of the simultaneous Pell equations x2-24y2=1 and y2 - pz2=1
Ai, Xiaochuan
Chen, Jianhua
Zhang, Silan
Hu, Hao
JOURNAL OF NUMBER THEORY, 2015, 147 : 103 - 108

← 1 2 3 4 5 →