Factorization and congruence in the arithmetics of Cayley's algebra

This paper treats factorization and congruence in the arithmetics of Cayley's algebra C. Results, proved by Rankin [10], on the number of factorizations of a given element in the nonmaximal arithmetics Ho and Jo are reviewed. Further, new results on congruence are established and are used to fi...

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Bibliographic Details
Published in:Glasgow mathematical journal 1991-05, Vol.33 (2), p.171-180
Main Author: Lamont, P. J. C.
Format: Article
Language:English
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Summary:This paper treats factorization and congruence in the arithmetics of Cayley's algebra C. Results, proved by Rankin [10], on the number of factorizations of a given element in the nonmaximal arithmetics Ho and Jo are reviewed. Further, new results on congruence are established and are used to find the number of factorizations of a prescribed element in the remaining arithmetics, including the maximal arithmetics Jw When computer factorizing a given element, the congruence results can be used as a heuristic device to prune the search tree.
ISSN:0017-0895
1469-509X
DOI:10.1017/S001708950000820X