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2020 Complete generalized Fibonacci sequences modulo primes
Mohammad Javaheri, Nikolai A. Krylov
Mosc. J. Comb. Number Theory 9(1): 1-15 (2020). DOI: 10.2140/moscow.2020.9.1

Abstract

We study generalized Fibonacci sequences F n + 1 = P F n Q F n 1 with initial values F 0 = 0 and F 1 = 1 . Let P , Q be relatively prime nonzero integers such that P 2 4 Q is not a perfect square. We show that if Q = ± 1 then the sequence { F n } n = 0 misses a congruence class modulo every large enough prime. If Q ± 1 , we prove under the GRH that the sequence { F n } n = 0 hits every congruence class modulo infinitely many primes.

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Mohammad Javaheri. Nikolai A. Krylov. "Complete generalized Fibonacci sequences modulo primes." Mosc. J. Comb. Number Theory 9 (1) 1 - 15, 2020. https://doi.org/10.2140/moscow.2020.9.1

Information

Received: 17 December 2018; Revised: 7 November 2019; Accepted: 22 November 2019; Published: 2020
First available in Project Euclid: 20 March 2020

zbMATH: 07171951
MathSciNet: MR4066555
Digital Object Identifier: 10.2140/moscow.2020.9.1

Subjects:
Primary: 11B39
Secondary: 11B50

Rights: Copyright © 2020 Mathematical Sciences Publishers

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