On perfect powers that are sums of two Pell numbers

被引：4

作者：

Aboudja, Hyacinthe ^{[1
]}

Hernane, Mohand ^{[2
]}

Rihane, Salah Eddine ^{[3
]}

Togbe, Main ^{[4
]}

机构：

[1] Oklahoma City Univ, Petree Coll Art & Sci PCAS, Comp Sci Dept, 2501 N Blackwelder, Oklahoma City, OK 73106 USA

[2] Univ Sci & Technol Houari Boumediene USTHB, Fac Math, Lab Algebre & Theorie Nombres, BP 32, Bab Ezzouar 16111, Algeria

[3] Univ Sci & Technol Houari Boumediene, Fac Math, Lab Algebra & Number Theory, BP 32, Algiers 16111, Algeria

[4] Purdue Univ Northwest, Dept Math Stat & Comp Sci, 1401 S,US 421, Westville, IN 46391 USA

来源：

PERIODICA MATHEMATICA HUNGARICA | 2021年 / 82卷 / 01期

关键词：

Perfect numbers; Exponential equations; Perfect powers; p-adic valuation;

D O I：

10.1007/s10998-020-00342-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Pk denote the kth term of the Pell sequence. In this paper we find all solutions of the exponential Diophantine equation Pn+Pm=ysP_n+P_m = y<^>s$$\end{document} in positive integer variables (m, n, y, s) under the assumption n equivalent to m(mod2).

引用

页码：11 / 15

页数：5

共 50 条

[1] On perfect powers that are sums of two Pell numbers
Hyacinthe Aboudja
Mohand Hernane
Salah Eddine Rihane
Alain Togbé
[J]. Periodica Mathematica Hungarica, 2021, 82 : 11 - 15
[2] Powers of Two as Sums of Three Pell Numbers
Bravo, Jhon J.
Faye, Bernadette
Luca, Florian
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2017, 21 (04): : 739 - 751
[3] PERFECT POWERS THAT ARE SUMS OF TWO POWERS OF FIBONACCI NUMBERS
Zhang, Zhongfeng
Togbe, Alain
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 99 (01) : 34 - 41
[4] On perfect powers that are sums of two Fibonacci numbers
Luca, Florian
Patel, Vandita
[J]. JOURNAL OF NUMBER THEORY, 2018, 189 : 90 - 96
[5] Sums of Fibonacci numbers that are perfect powers
Ziegler, Volker
[J]. QUAESTIONES MATHEMATICAE, 2023, 46 (08) : 1717 - 1742
[6] Pell and Pell–Lucas Numbers as Sums of Two Repdigits
Chèfiath Adegbindin
Florian Luca
Alain Togbé
[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43 : 1253 - 1271
[7] Pell and Pell-Lucas Numbers as Sums of Two Repdigits
Adegbindin, Chefiath
Luca, Florian
Togbe, Alain
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (02) : 1253 - 1271
[8] Perfect Pell powers
Cohn, JHE
[J]. GLASGOW MATHEMATICAL JOURNAL, 1996, 38 : 19 - 20
[9] Repdigits As Sums Of Two Associated Pell Numbers
Rayaguru, Sai Gopal
Panda, Gopal Krishna
[J]. APPLIED MATHEMATICS E-NOTES, 2021, 21 : 402 - 409
[10] Powers of Two as Sums of Two Lucas Numbers
Bravo, Jhon J.
Luca, Florian
[J]. JOURNAL OF INTEGER SEQUENCES, 2014, 17 (08)

← 1 2 3 4 5 →