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

Note on representing a prime as a sum of two squares


Author: John Brillhart
Journal: Math. Comp. 26 (1972), 1011-1013
MSC: Primary 10A25; Secondary 10A30
MathSciNet review: 0314745
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Abstract | References | Similar Articles | Additional Information

Abstract: An improvement is given to the method of Hermite for finding $ a$ and $ b$ in $ p = {a^2} + {b^2}$, where $ p$ is a $ {\text{prime}} \equiv 1\pmod 4$.


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

  • [1] C. Hermite, ``Note au sujet de l'article précédent,'' J. Math. Pures Appl., v. 1848, p. 15; also: ``Note sur un théorème rélatif aux nombres entières,'' Oevres. Vol. 1, p. 264.
  • [2] D. H. Lehmer, Computer technology applied to the theory of numbers, Studies in Number Theory, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1969, pp. 117–151. MR 0246815 (40 #84)
  • [3] Oskar Perron, Die Lehre von den Kettenbrüchen, Chelsea Publishing Co., New York, N. Y., 1950 (German). 2d ed. MR 0037384 (12,254b)
  • [4] J. A. Serret, ``Sur un théorème rélatif aux nombres entières,'' J. Math. Pures Appl., v. 1848, pp. 12-14.
  • [5] D. Shanks, Review of ``A table of Gaussian primes,'' by L. G. Diehl and J. H. Jordan, Math. Comp., v. 21, 1967, pp. 260-262.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0314745-6
PII: S 0025-5718(1972)0314745-6
Keywords: Algorithm, sum of two squares
Article copyright: © Copyright 1972 American Mathematical Society