On perfect powers that are sums of two Fibonacci numbers

JOURNAL OF NUMBER THEORY

卷:189

Article

Luca, Florian^1,2,3  Patel, Vandita⁴ 

[1] Univ Witwatersrand, Sch Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[3] Univ Ostrava, Dept Math, Fac Sci, 30 Dubna 22, CZ-70103 Ostrava 1, Czech Republic

[4] Univ Toronto, Dept Math, Bahen Ctr, 40 St George St,Room 6290, Toronto, ON M5S 2E4, Canada

关键词: Exponential equation;    Hemachandra numbers;    Fibonacci numbers;   

DOI  :  10.1016/j.jnt.2018.02.003

来源: Elsevier

【 摘 要 】

We study the equation F-n + F-m = y(p), where F-n, and F-m are respectively the n-th and m-th Fibonacci numbers and p >= 2. We find all solutions under the assumption n equivalent to (mod 2). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free