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

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

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]**J. BRILLHART, "Note on representing a prime as a sum of two squares,"*Math. Comp.*, v. 26, 1972, pp. 1011-1013. MR**0314745 (47:3297)****[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]**L. J. MORDELL,*Diophantine Equations*, Academic Press, New York, 1969. MR**0249355 (40:2600)****[4]**H. M. STARK, "On complex quadratic fields with class number two,"*Math. Comp.*, v. 29, 1975, pp. 289-302. MR**0369313 (51:5548)**

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

Article copyright:
© Copyright 1980
American Mathematical Society