On the representation of N by the powers of the golden mean and Zeckendorf theorem

Edward Zhu

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arXiv · 2308.06364

On the representation of N by the powers of the golden mean and Zeckendorf theorem

Edward Zhu

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Abstract

It is well known that every positive integer N can be written as the sum of non-consecutive powers of the golden ratio. We prove that the non-positive powers, together with the parity of the first positive power, can determine the positive integer. We give an explicit formula for N in terms of the above information.

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Edward Zhu. 2023-08-09. On the representation of N by the powers of the golden mean and Zeckendorf theorem. https://arxiv.org/abs/2308.06364

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