On the complementary factor in a new congruence algorithm
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 thi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000140 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |