On the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss

Kwok Chi Chim; Volker Ziegler

On the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss

Kwok Chi Chim
, Volker Ziegler

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Abstract

Let F_n denote the n-th Fibonacci number, and p_i the i-th prime number. In this paper, we consider the Diophantine equation F_n1 + F_n2 + F_n3 = p^z1₁ · · · p^zs_s in non-negative integers n₁ ≥ n₂ ≥ n₃ ≥ 0 and non-negative integers zi with 1 ≤ i ≤ s. In particular, we completely solve the case that s = 12.

Original language	English
Pages (from-to)	407-434
Number of pages	28
Journal	Publicationes Mathematicae Debrecen
Volume	103
Issue number	3-4
Publication status	Published - 2023

Keywords

diophantine equations
fibonacci sequences
linear forms in logarithms
recurrence sequences

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2023 02 06 Chim et al Diophantine acceptedAccepted author manuscript, 388 KB

https://publi.math.unideb.hu/contents.php?szam=2023+%2F+103+%2F+3-4

Cite this

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title = "On the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss",

abstract = "Let Fn denote the n-th Fibonacci number, and pi the i-th prime number. In this paper, we consider the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss in non-negative integers n1 ≥ n2 ≥ n3 ≥ 0 and non-negative integers zi with 1 ≤ i ≤ s. In particular, we completely solve the case that s = 12.",

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T1 - On the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss

AU - Chim, Kwok Chi

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Y1 - 2023

N2 - Let Fn denote the n-th Fibonacci number, and pi the i-th prime number. In this paper, we consider the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss in non-negative integers n1 ≥ n2 ≥ n3 ≥ 0 and non-negative integers zi with 1 ≤ i ≤ s. In particular, we completely solve the case that s = 12.

AB - Let Fn denote the n-th Fibonacci number, and pi the i-th prime number. In this paper, we consider the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss in non-negative integers n1 ≥ n2 ≥ n3 ≥ 0 and non-negative integers zi with 1 ≤ i ≤ s. In particular, we completely solve the case that s = 12.

KW - diophantine equations

KW - fibonacci sequences

KW - linear forms in logarithms

KW - recurrence sequences

M3 - Article

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SP - 407

EP - 434

JO - Publicationes Mathematicae Debrecen

JF - Publicationes Mathematicae Debrecen

IS - 3-4

ER -

On the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss

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Keywords

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