The Proof of a Conjecture Related to Divisibility Properties of z(n)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018557" target="_blank" >RIV/62690094:18470/21:50018557 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/9/20/2638" target="_blank" >https://www.mdpi.com/2227-7390/9/20/2638</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math9202638" target="_blank" >10.3390/math9202638</a>

Result language
angličtina
Original language name
The Proof of a Conjecture Related to Divisibility Properties of z(n)
Original language description
The order of appearance of n (in the Fibonacci sequence) z(n) is defined as the smallest positive integer k for which n divides the k-the Fibonacci number F-k. Very recently, TrojovskATIN SMALL LETTER Y WITH ACUTE proved that z(n) is an even number for almost all positive integers n (in the natural density sense). Moreover, he conjectured that the same is valid for the set of integers n & GE;1 for which the integer 4 divides z(n). In this paper, among other things, we prove that for any k & GE;1, the number z(n) is divisible by 2(k) for almost all positive integers n (in particular, we confirm TrojovskATIN SMALL LETTER Y WITH ACUTE's conjecture).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)