An efficient algorithmic solution of the Diophantine equation

Author:
Peter Wilker

Journal:
Math. Comp. **35** (1980), 1347-1352

MSC:
Primary 10B05; Secondary 10-04, 10A25

MathSciNet review:
583512

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Abstract: The determination of irreducible elements of the domain requires the solution of the Diophantine equation , where *m* represents certain primes or products of two primes. An algorithm of order is given for the solution of the equation.

**[1]**John Brillhart,*Note on representing a prime as a sum of two squares*, Math. Comp.**26**(1972), 1011–1013. MR**0314745**, 10.1090/S0025-5718-1972-0314745-6**[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****[3]**L. J. Mordell,*Diophantine equations*, Pure and Applied Mathematics, Vol. 30, Academic Press, London-New York, 1969. MR**0249355****[4]**H. M. Stark,*On complex quadratic fields wth class-number two*, Math. Comp.**29**(1975), 289–302. Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday. MR**0369313**, 10.1090/S0025-5718-1975-0369313-X

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0583512-5

Article copyright:
© Copyright 1980
American Mathematical Society