Primes as sums of Fibonacci numbers

Activity: Talk or presentation › Oral presentation

Description

We discuss the relationship between prime numbers and sums of Fibonacci numbers. One of our main results says that for every sufficiently large integer there exists a prime number that can be represented as the sum of different and non-consecutive Fibonacci numbers. We are concerned with the Zeckendorf sum-of-digits function z, which returns the minimal number of Fibonacci numbers needed to write a positive integer as their sum. The proof of such a prime number theorem for z, combined with a corresponding local result, constitutes our central contribution.
Period25 Mar 2025
Held atJagiellonian University, Krakow, Poland
Degree of RecognitionRegional

Keywords

  • Zeckendorf expansion
  • sum-of-digits function
  • prime number theorem
  • Mőbius orthogonality