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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] Ronald Alter, Thaddeus B. Curtz, and K. K. Kubota, Remarks and results on congruent numbers, Proceedings of the Third Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1972), Florida Atlantic Univ., Boca Raton, Fla., 1972, pp. 27–35. MR 0349554
  • [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 Applied Mathematics, Vol. 30, Academic Press, London-New York, 1969. MR 0249355
  • [6] J. V. Uspensky & M. A. Heaslet, Elementary Number Theory, McGraw-Hill, New York, 1939. MR 1, 38.

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Keywords: Congruent numbers, Diophantine equation
Article copyright: © Copyright 1974 American Mathematical Society