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arXiv · 2512.12841

Further Extensions of Sury's Identity

Gregory Dresden·Xiaoya Gao
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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.

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Gregory Dresden, Xiaoya Gao. 2025-12-14. Further Extensions of Sury's Identity. https://arxiv.org/abs/2512.12841

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