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On Pascal triangles modulo a prime power

✍ Scribed by Alexis Bés

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
975 KB
Volume
89
Category
Article
ISSN
0168-0072

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✦ Synopsis

In the first part of the paper we study arithmetical properties of Pascal triangles module a prime power; the main result is the generalization of Lucas' theorem. Then we investigate the structure (N; B,.), where p is a prime, a is an integer greater than one, and B,.(x, ~1) = Rem((":'), p"); it is shown that addition is first-order definable in this structure, and that its elementary theory is decidable.

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