Skip to main content

New very large amicable pairs

Part of the Lecture Notes in Mathematics book series (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, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • 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

Learn about 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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

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