descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 24 Nov 2014Embargo end date: 01 Jan 2014 English Publisher:World Scientific Pub Co Pte LtJournal:International Journal of Number Theory, volume 11, pages 159-169 (issn: 1793-0421, eissn: 1793-7310,

Authors: Tianxin Cai; Deyi Chen; Yong Zhang;

doi: 10.1142/s1793042115500098 , 10.48550/arxiv.1406.5684 , 10.48550/arxiv.1310.0898 , 10.48550/arxiv.1709.06337

arXiv: http://arxiv.org/abs/1709.06337 , http://arxiv.org/abs/1406.5684 , http://arxiv.org/abs/1310.0898

Perfect numbers and Fibonacci primes (I)

- Summary
- Subjects
- Metrics

Abstract

In this paper, we introduce the concept of F-perfect number, which is a positive integer n such that ∑d|n,d<n d2 = 3n. We prove that all the F-perfect numbers are of the form n = F2k-1 F2k+1, where both F2k-1 and F2k+1 are Fibonacci primes. Moreover, we obtain other interesting results and raise a new conjecture on perfect numbers.

Related Organizations

Zhejiang Ocean University
China (People's Republic of)

Keywords

Mathematics - Number Theory, 11B83, 11D09, 11D25, FOS: Mathematics, Number Theory (math.NT), Primary 11B83, Secondary 11D09, 11D25

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	1
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average