On the complementary factor in a new congruence algorithm

Autor: Peter Hilton, Jean Pedersen
Jazyk: angličtina
Rok vydání: 1987
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 10, Iss 1, Pp 113-123 (1987)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171287000140
Popis: In an earlier paper the authors described an algorithm for determining the quasi-order, Qt(b), of tmodb, where t and b are mutually prime. Here Qt(b) is the smallest positive integer n such that tn=±1modb, and the algorithm determined the sign (−1) ϵ , ϵ =0,1, on the right of the congruence. In this sequel we determine the complementary factor F such that tn−(−1) ϵ =bF, using the algorithm rather that b itself. Thus the algorithm yields, from knowledge of b and t, a rectangular array a1a2…ark1k2…kr ϵ 1 ϵ 2… ϵ rq1q2…qr The second and third rows of this array determine Qt(b) and ϵ ; and the last 3 rows of the array determine F. If the first row of the array is multiplied by F, we obtain a canonical array, which also depends only on the last 3 rows of the given array; and we study its arithmetical properties.
Databáze: Directory of Open Access Journals
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