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Mathematics > History and Overview

arXiv:2409.01296 (math)
[Submitted on 2 Sep 2024]

Title:Fibonacci Partial Sums Tricks

Authors:Nikhil Byrapuram, Adam Ge, Selena Ge, Tanya Khovanova, Sylvia
Zia Lee, Rajarshi Mandal, Gordon Redwine, Soham Samanta, Daniel Wu,
Danyang Xu, Ray Zhao
View a PDF of the paper titled Fibonacci Partial Sums Tricks, by
Nikhil Byrapuram and 10 other authors
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    Abstract:The following magic trick is at the center of this
    paper. While the audience writes the first ten terms of a
    Fibonacci-like sequence (the sequence following the same
    recursion as the Fibonacci sequence), the magician calculates the
    sum of these ten terms very fast by multiplying the 7th term by
    11. This trick is based on the divisibility properties of partial
    sums of Fibonacci-like sequences. We find the maximum Fibonacci
    number that divides the sum of the Fibonacci numbers 1 through
    $n$. We discuss the generalization of the trick for other
    second-order recurrences. We show that a similar trick exists for
    Pell-like sequences and does not exist for Jacobhstal-like
    sequences.

Comments:    26 pages, 9 tables
Subjects:    History and Overview (math.HO); Number Theory (math.NT)
MSC classes: 11B39 (Primary) 00A08
Cite as:     arXiv:2409.01296 [math.HO]
             (or arXiv:2409.01296v1 [math.HO] for this version)
             https://doi.org/10.48550/arXiv.2409.01296
             Focus to learn more
             arXiv-issued DOI via DataCite

Submission history

From: Tanya Khovanova [view email]
[v1] Mon, 2 Sep 2024 14:38:49 UTC (20 KB)
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