Determination of principal factors in and

Author:
H. C. Williams

Journal:
Math. Comp. **38** (1982), 261-274

MSC:
Primary 12A30; Secondary 12A45

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637306-4

MathSciNet review:
637306

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Abstract: Let or 3 and let *D* be a positive *l*-power-free integer. Also, let *R* be the product of all the rational primes which completely ramify in . The integer *d* is a principal factor of the discriminant of *K* if , where is an algebraic integer of *K* and . In this paper algorithms for finding these principal factors are described. Special attention is given to the case of , where it is shown that Voronoi's continued fraction algorithm can be used to find principal factors. Some results of a computer search for principal factors for all with are also presented.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637306-4

Keywords:
Principal factors,
Voronoi's algorithm,
Diophantine equations

Article copyright:
© Copyright 1982
American Mathematical Society