An efficient algorithmic solution of the Diophantine equation $u^{2}+5v^{2}=m$
Author:
Peter Wilker
Journal:
Math. Comp. 35 (1980), 1347-1352
MSC:
Primary 10B05; Secondary 10-04, 10A25
DOI:
https://doi.org/10.1090/S0025-5718-1980-0583512-5
MathSciNet review:
583512
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The determination of irreducible elements of the domain $Z[\sqrt { - 5} ]$ requires the solution of the Diophantine equation ${u^2} + 5{v^2} = m$, where m represents certain primes or products of two primes. An algorithm of order $\log m$ is given for the solution of the equation.
- John Brillhart, Note on representing a prime as a sum of two squares, Math. Comp. 26 (1972), 1011–1013. MR 314745, DOI https://doi.org/10.1090/S0025-5718-1972-0314745-6
- 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
- L. J. Mordell, Diophantine equations, Pure and Applied Mathematics, Vol. 30, Academic Press, London-New York, 1969. MR 0249355
- H. M. Stark, On complex quadratic fields wth class-number two, Math. Comp. 29 (1975), 289–302. MR 369313, DOI https://doi.org/10.1090/S0025-5718-1975-0369313-X
Retrieve articles in Mathematics of Computation with MSC: 10B05, 10-04, 10A25
Retrieve articles in all journals with MSC: 10B05, 10-04, 10A25
Additional Information
Article copyright:
© Copyright 1980
American Mathematical Society
