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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A note on congruent numbers


Authors: Ronald Alter and Thaddeus B. Curtz
Journal: Math. Comp. 28 (1974), 303-305
MSC: Primary 10B05
Corrigendum: Math. Comp. 30 (1976), 198.
MathSciNet review: 0337758
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Abstract | References | Similar Articles | Additional Information

Abstract: An integer a is called a congruent number if and only if there are positive integer solutions to the system of equations

$\displaystyle {x^2} + a{y^2} = {z^2}\quad {\text{and}}\quad {x^2} - a{y^2} = {t^2}.$

In this note congruent numbers are discussed and a table of known square-free congruent numbers less than 1000 is exhibited.

References [Enhancements On Off] (What's this?)

  • [1] R. Alter, T. B. Curtz & K. K. Kubota, Remarks and Results on Congruent Numbers, Proc. Third Southeastern Conference on Combinatorics, Graph Theory and Computing, 1972, pp. 27-35. MR 0349554 (50:2047)
  • [2] L. Bastien, "Nombres congruents," Intermédiare des Math., v. 22, 1915, pp. 231-232.
  • [3] L. E. Dickson, History of the Theory of Numbers. Vol. II, Carnegie Institute of Washington, 1920.
  • [4] A. Gérardin, "Nombres congruents," Intermédiare des Math., v. 22, 1915, pp. 52-53.
  • [5] L. J. Mordell, Diophantine Equations, Pure and Appl. Math., vol. 30, Academic Press, New York, 1969. MR 40 #2600. MR 0249355 (40:2600)
  • [6] J. V. Uspensky & M. A. Heaslet, Elementary Number Theory, McGraw-Hill, New York, 1939. MR 1, 38.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0337758-9
PII: S 0025-5718(1974)0337758-9
Keywords: Congruent numbers, Diophantine equation
Article copyright: © Copyright 1974 American Mathematical Society