New notes on the equation d(n) = d(φ(n)) and the inequality d(n) > d(φ(n))

被引：1

作者：

Bellaouar, Djamel ^{[1
]}

Togbe, Alain ^{[2
]}

Jakimczuk, Rafael ^{[3
]}

机构：

[1] Univ 8 Mai 1945 Guelma, Dept Math, BP 401, Guelma 24000, Algeria

[2] Purdue Univ Northwest, Dept Math & Stat, 2200 169th St, Hammond, IN 46323 USA

[3] Univ Nacl Lujan, Div Matemat, Buenos Aires, Argentina

来源：

MATHEMATICA SLOVACA | 2024年 / 74卷 / 05期

关键词：

Divisor function; Euler's function; prime numbers; Diophantine equations;

D O I：

10.1515/ms-2024-0081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let d(n) and phi(n) denote the number of positive divisors of n and the Euler's phi function of n, respectively. In this paper, we prove various (conditional and unconditional) results about the solvability of the Diophantine equation d(n) = d(phi(n)) and a related inequality. For further research, we present some open problems.

引用

页码：1127 / 1146

页数：20

共 9 条

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Amroune, Zahra
Bellaouar, Djamel
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[J]. NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2023, 29 (02) : 284 - 309
[2] Notes on the Equation d(n) = d(φ(n)) and Related Inequalities
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[J]. MATHEMATICA SLOVACA, 2023, 73 (03) : 613 - 632
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[9] On certain equations and inequalities involving the arithmetical functions φ(n) and d(n)
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[J]. NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2022, 28 (02) : 376 - 379

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