Products of three Fibonacci numbers that are repdigits

被引：0

作者：

Alan, Murat ^{[1
]}

Alan, Kadriye Simsek ^{[2
]}

机构：

[1] Yildiz Tech Univ, Dept Math, Istanbul, Turkiye

[2] Yildiz Tech Univ, Dept Math Engn, Istanbul, Turkiye

来源：

ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL | 2023年 / 16卷 / 04期

关键词：

Fibonacci numbers; Diophantine equations; Repdigits; Linear forms in logarithms; SUMS; EQUATIONS;

D O I：

10.32513/asetmj/193220082333

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (F-n)(n >= 0) be a Fibonacci sequence. A non-negative integer whose digits are all equal is called a repdigit and any non-zero repdigit is of the form a (10(d) -1/9) where 1 <= a <= 9 and 1 <= d. In this paper, we search all repdigits that can be written as products of three Fibonacci numbers. As a mathematical expression, we find all non-negative integer solutions (n, m, l, a, d) of the Diophantine equation FnFmFl = a (10(d) -1/9) , 1 <= l <= m <= n and 1 <= a <= 9..

引用

页码：57 / 66

页数：10

共 50 条

[41] On Mulatu and generalized Lucas numbers which are products of four b-repdigits with a consequence
Adedji, Kouessi Norbert
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2025,
[42] Repdigits base b as products of two Pell numbers or Pell-Lucas numbers
Erduvan, Fatih
Keskin, Refik
Siar, Zafer
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2021, 27 (03):
[43] Pell and Pell-Lucas numbers which are concatenations of three repdigits
Erduvan, Fatih
Duman, Merve Guney
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2024,
[44] Fibonacci Numbers with a Prescribed Block of Digits
Trojovsky, Pavel
MATHEMATICS, 2020, 8 (04)
[45] Product of repdigits with consecutive lengths in the Fibonacci sequence.
Jhonny C. Gómez
Florian Luca
Boletín de la Sociedad Matemática Mexicana, 2021, 27
[46] Repdigits as Sums of Four Tribonacci Numbers
Zhou, Yuetong
Yang, Peng
Zhang, Shaonan
Zhang, Kaiqiang
SYMMETRY-BASEL, 2022, 14 (09):
[47] PADOVAN NUMBERS AS SUM OF TWO REPDIGITS
Duman, Merve Guney
Keskin, Refik
Hocaoglu, Leman
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2023, 76 (09): : 1326 - 1334
[48] Product of repdigits with consecutive lengths in the Fibonacci sequence.
Gomez, Jhonny C.
Luca, Florian
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2021, 27 (02):
[49] FIBONACCI NUMBERS THAT ARE η-CONCATENATIONS OF LEONARDO AND LUCAS NUMBERS
Taher, Hunar Sherzad
Dash, Saroj Kumar
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2025, 78 (02): : 171 - 180
[50] ON FACTORIALS EXPRESSIBLE AS SUMS OF AT MOST THREE FIBONACCI NUMBERS
Luca, Florian
Siksek, Samir
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2010, 53 : 747 - 763

← 1 2 3 4 5 →