The density of primes \(P\), such that \(-1\) is a residue modulo \(P\) of two consecutive Fibonacci numbers, is \(2/3\)

DOI10.1216/rmjm/1181071607zbMath0979.11007OpenAlexW2027085992MaRDI QIDQ1974414

Christian Ballot

Publication date: 4 September 2000

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL29-3/CONT29-3/CONT29-3.html

zbMATH Keywords

Fibonacci sequencelinear recurrence sequencedensity of prime maximal divisorsFibonacci residues

Mathematics Subject Classification ID

Recurrences (11B37) Special sequences and polynomials (11B83) Density, gaps, topology (11B05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

• Unnamed Item
• Unnamed Item
• The set of primes dividing the Lucas numbers has density 2/3
• Group structure and maximal division for cubic recursions with a double root
• Über die Dichte der Primzahlen \(p\), für die eine vorgegebene ganzrationale Zahl \(a\neq 0\) von gerader bzw. ungerader Ordnung \(\mod p\) ist
• On groups of linear recurrences. I
• The prime divisors of Fibonacci numbers
• New Primality Criteria and Factorizations of 2 m ± 1
• Density of prime divisors of linear recurrences
• Note on Representing a Prime as a Sum of Two Squares
• The Maximal Prime Divisors of Linear Recurrences

This page was built for publication: The density of primes \(P\), such that \(-1\) is a residue modulo \(P\) of two consecutive Fibonacci numbers, is \(2/3\)