Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
article
Free access

Congruent numbers: from elementary to algebraic number theory

Published: 01 November 1984 Publication History

Abstract

Since nowadays electronic high speed computers of various sizes and types are commonly used at schools of all levels it appears to be in order to propose some appropriate mathematical problems which can be approached by means of a computer. For students this way of attacking such problems is certainly a valuable experience and should become an essential part of their scientific education.

References

[1]
{ACK} Alter, R., Curtz, T. B., Kubota, K. K.: Remarks and results on congruent numbers. Proc. Third Southeastern Conf. on Combinatorics, Graph Theory and Computing 1972, pp. 27--35.
[2]
{AC} Alter, R., Curtz, T. B.: A note on congruent numbers. Math. Comp. 28 (1974), 303--305.
[3]
{B} Bastien, L.: Nombres congruents. Intermédiaire des Math. 22 (1915), 231--232.
[4]
{CW} Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. math. 39 (1977), 223--251.
[5]
{D}Dickson, L. E.: History of the theory of numbers II. Carnegie Institution, Washington, DC (1920); reprinted by Chelsea 1966.
[6]
{G} Gérardin, A.: Nombres congruent. Intermédiaire des Math. 22 (1915, 52--53.
[7]
{L1} Lagrange, J.: Nombres congruents et courbes elliptiques. Sém. Delange-Pisot-Poitou (Théorie des nombres) 16e année, 1974/75, no. 16, 17 p.
[8]
{L2} Lagrange, J.: Construction d'une table de nombres congruents. Manuscript, Reims.
[9]
{La} Lang, S.: Elliptic Curves: Diophantine Analysis. Springer-Verlag, Berlin-Heidelberg-New York 1978.
[10]
{O} Olson, L. D.: Points of finite order on elliptic curves with complex multiplication. Manuscripta math. 14 (1974), 195--205.
[11]
{S} Stephens, N. M.: Congruence properties of congruent numbers. Bull. London Math. Soc. 7 (1975), 182--184.
[12]
{T} Tunnell, J. B.: A classical diophantine problem and modular forms of weight 3/2. Invent. math. 72 (1983), 323--334.

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM SIGSAM Bulletin
ACM SIGSAM Bulletin  Volume 18-19, Issue 4-1
November-February 1984-1985
59 pages
DOI:10.1145/1089355
Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 November 1984
Published in SIGSAM Volume 18-19, Issue 4-1

Check for updates

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 310
    Total Downloads
  • Downloads (Last 12 months)29
  • Downloads (Last 6 weeks)2
Reflects downloads up to 13 Sep 2024

Other Metrics

Citations

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media