Skip to main content
Springer Nature Link
Log in

Ramanujan’s taxicab number and its ilk

  • Published:
The Ramanujan Journal Aims and scope Submit manuscript

Abstract

We discuss properties of the Hardy-Ramanujan taxicab number, 1729, and similar numbers. The similar numbers include Carmichael numbers, Lucas Carmichael numbers, sums of cubes, and integers of the form \(b^n\pm 1\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

The full Table 2, with all 164 numbers, is at https://homes.cerias.purdue.edu/~ssw/taxitab2.txt.

References

  1. Alford, W.R.: Andrew Granville, and Carl Pomerance: there are infinitely many Carmichael numbers. Ann. Math. 139, 703–722 (1994). https://doi.org/10.2307/2118576. (JSTOR 2118576)

    Article  MathSciNet  Google Scholar 

  2. Banks, W., Finch, C., Lucas, F., Pomerance, C., Stǎnicǎ, P.: Sierpiński and Carmichael numbers. Trans. Am. Math. Soc. 367, 355–376 (2015)

    Article  Google Scholar 

  3. Brillhart, J., Lehmer, D.H., Selfridge, J.L., Tuckerman, B., Wagstaff, Jr, S.S.: Factorizations of \(b^n \pm 1\), \(b\) = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers, 2nd edition. Amer. Math. Soc., Providence, Rhode Island (1988)

  4. Bernstein, D.J.: Enumerating solutions to \(p(a)+q(b)=r(c)+s(d)\). Math. Comput. 70, 389–394 (2001)

    Article  MathSciNet  Google Scholar 

  5. Korselt, A.: Probléme chinois. L’Intermédiaire des Mathématiciens 3, 142–143 (1899)

    Google Scholar 

  6. OEIS Foundation Inc.: The On-Line Encyclopedia of Integer Sequences (2023). https://oeis.org

  7. Pinch, R.G.E.: The Carmichael numbers up to \(10^{21}\), Proceedings of the Conference on Algorithmic Number Theory, 46, Turku, Finland: Turku Center for Computer Science, pp. 129–131 (2007)

  8. Wagstaff, S.S., Jr.: The Joy of Factoring. Student Mathematical Library, vol. 68. American Mathematical Society, Providence, Rhode Island (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Education and Research in Information Assurance and Security and Department of Computer Sciences Purdue University, West Lafayette, IN, 47907-1398, USA

    Samuel S. Wagstaff Jr.

Authors
  1. Samuel S. Wagstaff Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Samuel S. Wagstaff Jr..

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported by the CERIAS Center at Purdue University.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wagstaff, S.S. Ramanujan’s taxicab number and its ilk. Ramanujan J 64, 761–764 (2024). https://doi.org/10.1007/s11139-024-00846-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11139-024-00846-1

Keywords

Mathematics Subject Classification

Search

Navigation