Fibonacci Partial Sums Tricks
History and Overview
2024-09-04 v1 Number Theory
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 . 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.
Cite
@article{arxiv.2409.01296,
title = {Fibonacci Partial Sums Tricks},
author = {Nikhil Byrapuram and Adam Ge and Selena Ge and Tanya Khovanova and Sylvia Zia Lee and Rajarshi Mandal and Gordon Redwine and Soham Samanta and Daniel Wu and Danyang Xu and Ray Zhao},
journal= {arXiv preprint arXiv:2409.01296},
year = {2024}
}
Comments
26 pages, 9 tables