A variation on the theme of Nicomachus
Florian Luca, Gerem\'ias Polanco, Wadim Zudilin
TL;DR
This paper proves conjectures related to the first and third moments of Beatty sequences involving the golden ratio and its square, advancing understanding of their mathematical properties.
Contribution
It provides proofs for conjectures by K. Stolarsky on moments of Beatty sequences with specific irrational numbers.
Findings
Confirmed conjectures on the moments of Beatty sequences
Established new properties of sequences involving the golden ratio
Enhanced theoretical understanding of Beatty sequences with irrational parameters
Abstract
We prove some conjectures of K. Stolarsky concerning the first and third moment of the Beatty sequences with the golden section and its square.
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