Skip to main content
SpringerLink
Log in

New very large amicable pairs

  • Conference paper
  • First Online:
Number Theory Noordwijkerhout 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1068))

Abstract

Computations are described which led to the discovery of many very large amicable pairs, which are much larger than the largest amicable pair thus far known.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adleman, L.M., C. Pomerance & R.S. Rumely, On distinguishing prime numbers from composite numbers, Ann. Math. 117 (1983), 173–206.

    Article  MathSciNet  MATH  Google Scholar 

  2. Borho, W., Grosse Primzahlen und befreundete Zahlen: über den Lucas-Test und Thabit-Regeln, to appear in Mitt. Math. Gesells. Hamburg.

    Google Scholar 

  3. Borho, W., On Thabit ibn Kurrah’s formula for amicable numbers, Math. Comp. 26 (1972), 571–578.

    MathSciNet  MATH  Google Scholar 

  4. Borho, W., Some large primes and amicable numbers, Math. Comp. 36 (1981), 303–304.

    Article  MathSciNet  MATH  Google Scholar 

  5. Cohen, H. & H.W. Lenstra, Jr., Primality testing and Jacobi sums, Math. Comp. 42 (1984), 297–330.

    Article  MathSciNet  MATH  Google Scholar 

  6. Escott, E.B., Amicable numbers, Scripta Math. 12 (1946), 61–72.

    MathSciNet  MATH  Google Scholar 

  7. Euler, L., De numeris amicabilibus, Leonhardi Euleri Opera Omnia, Teubner, Leipzig and Berlin, Ser. I, vol. 2, 1915, 63–162.

    Google Scholar 

  8. Lee, E.J. & J.S. Madachy, The history and discovery of amicable numbers, J. Recr. Math. 5 (1972), Part I: 77–93, Part II: 153–173, Part III: 231–249.

    MathSciNet  MATH  Google Scholar 

  9. Ore, O., Number theory and its history, McGraw-Hill Book Company, New York etc. 1948.

    MATH  Google Scholar 

  10. Riele, H.J.J. te, Four large amicable pairs, Math. Comp. 28 (1974), 309–312.

    Article  MathSciNet  MATH  Google Scholar 

  11. Riele, H.J.J. te, On generating new amicable pairs from given amicable pairs, Math. Comp. 42 (1984), 219–223.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Herman J. J. te Riele

Authors
  1. Herman J. J. te Riele
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hendrik Jager

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

te Riele, H.J.J. (1984). New very large amicable pairs. In: Jager, H. (eds) Number Theory Noordwijkerhout 1983. Lecture Notes in Mathematics, vol 1068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099454

Download citation

  • DOI: https://doi.org/10.1007/BFb0099454

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13356-8

  • Online ISBN: 978-3-540-38906-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation