Skip to main content Accessibility help
×
Home
Hostname: page-component-dc8c957cd-b82tz Total loading time: 0.233 Render date: 2022-01-27T00:42:15.224Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

A VARIATION ON THE THEME OF NICOMACHUS

Published online by Cambridge University Press:  28 March 2018

FLORIAN LUCA
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany Department of Mathematics, Faculty of Sciences, University of Ostrava, 30 dubna 22, 701 03 Ostrava 1, Czech Republic email Florian.Luca@wits.ac.za
GEREMÍAS POLANCO
Affiliation:
School of Natural Science, Hampshire College, 893 West St, Amherst, MA 01002, USA email gpeNS@hampshire.edu
WADIM ZUDILIN*
Affiliation:
IMAPP, Radboud Universiteit, PO Box 9010, 6500 GL Nijmegen, The Netherlands School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia email w.zudilin@math.ru.nl, wadim.zudilin@newcastle.edu.au
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we prove some conjectures of K. Stolarsky concerning the first and third moments of the Beatty sequences with the golden section and its square.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2018 Australian Mathematical Publishing Association Inc.

Footnotes

The first author was supported in part by NRF (South Africa) Grant CPRR160325161141 and an A-rated researcher award, and by CGA (Czech Republic) Grant 17-02804S. The second author was supported in part by the Institute of Mathematics of Universidad Autonoma de Santo Domingo, Grant FONDOCyT 2015-1D2-186, Ministerio de Educación Superior Ciencia y Tecnología (Dominican Republic).

References

Kimberling, C., ‘The Zeckendorf array equals the Wythoff array’, Fibonacci Quart. 33 (1995), 38.Google Scholar
Stopple, J., A Primer of Analytic Number Theory. From Pythagoras to Riemann (Cambridge University Press, Cambridge, 2003).CrossRefGoogle Scholar
Warnaar, S. O., ‘On the q-analogue of the sum of cubes’, Electron. J. Combin. 11(1) (2004), Note 13, 2 pages.Google Scholar
You have Access
Open access
1
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A VARIATION ON THE THEME OF NICOMACHUS
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

A VARIATION ON THE THEME OF NICOMACHUS
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

A VARIATION ON THE THEME OF NICOMACHUS
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *