Primes as Sums of Fibonacci Numbers

Michael Drmota; Clemens Müllner; Lukas Spiegelhofer

Primes as Sums of Fibonacci Numbers

Michael Drmota
, Clemens Müllner
, Lukas Spiegelhofer

Chair of Mathematics, Statistics and Geometry (380)

Institute of Materials Science and Technology

Research output: Contribution to journal › Article › Research › peer-review

Abstract

We prove that, for a large enough integer k, there exist prime numbers that are the sum of exactly k different, non-consecutive Fibonacci numbers.
Along the way, we prove that the level of distribution of the Zeckendorf sum-of-digits function equals 1.

Translated title of the contribution	Darstellung von Primzahlen als Summe von Fibonacci-Zahlen
Original language	English
Number of pages	138
Journal	Memoirs of the American Mathematical Society
Volume	2025
Issue number	1537
Publication status	Published - 2025

Keywords

prime numbers
Fibonacci numbers
level of distribution

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https://arxiv.org/abs/2109.04068Licence: Other

Cite this

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title = "Primes as Sums of Fibonacci Numbers",

abstract = "We prove that, for a large enough integer k, there exist prime numbers that are the sum of exactly k different, non-consecutive Fibonacci numbers. Along the way, we prove that the level of distribution of the Zeckendorf sum-of-digits function equals 1.",

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AU - Müllner, Clemens

AU - Spiegelhofer, Lukas

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N2 - We prove that, for a large enough integer k, there exist prime numbers that are the sum of exactly k different, non-consecutive Fibonacci numbers. Along the way, we prove that the level of distribution of the Zeckendorf sum-of-digits function equals 1.

AB - We prove that, for a large enough integer k, there exist prime numbers that are the sum of exactly k different, non-consecutive Fibonacci numbers. Along the way, we prove that the level of distribution of the Zeckendorf sum-of-digits function equals 1.

KW - prime numbers

KW - Fibonacci numbers

KW - level of distribution

UR - https://doi.org/10.1090/memo/1537

M3 - Article

SN - 0065-9266

VL - 2025

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

IS - 1537

ER -

Primes as Sums of Fibonacci Numbers

Abstract

Keywords

Access to Document

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