Further Extensions of Sury's Identity
Number Theory
2026-05-12 v2 Combinatorics
Abstract
The equation commonly known as Sury's identity is a deceptively simple summation formula that connects the Lucas numbers, Fibonacci numbers, and powers of two. Many authors have given extensions and generalizations over the years; in this paper, we take a different approach that allows us to produce a good number of new summation formulas, all from elementary (but non-trivial) methods.
Cite
@article{arxiv.2512.12841,
title = {Further Extensions of Sury's Identity},
author = {Gregory Dresden and Xiaoya Gao},
journal= {arXiv preprint arXiv:2512.12841},
year = {2026}
}
Comments
22 pages