English

Fibonacci system and residue completeness

Number Theory 2013-07-12 v3

Abstract

We give necessary and sufficient conditions for a Fibonacci cycle to be residue complete (nondefective). In particular, the Lucas numbers modulo m is residue complete if and only if m = 2,4,6,7,14 or a power of 3.

Cite

@article{arxiv.1304.2892,
  title  = {Fibonacci system and residue completeness},
  author = {Cheng Lien Lang and Mong Lung Lang},
  journal= {arXiv preprint arXiv:1304.2892},
  year   = {2013}
}

Comments

We revise the article and give a direct proof of the main results

R2 v1 2026-06-21T23:57:11.248Z