منابع مشابه
On Decidability Within the Arithmetic of Addition and Divisibility
The arithmetic of natural numbers with addition and divisibility has been shown undecidable as a consequence of the fact that multiplication of natural numbers can be interpreted into this theory, as shown by J. Robinson [Rob49]. The most important decidable subsets of the arithmetic of addition and divisibility are the arithmetic of addition, proved by M. Presburger [Pre29], and the purely exi...
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1 Integers. Divisibility The cryptographic constructions we’re going to see in further lectures and courses are built on top of various algebraic structures. All these structures, however, are ultimately built on top of integers. The set of integers is Z = {. . . ,−2,−1, 0, 1, 2, . . .}. On this integers set, we are given the binary operations “+” (addition) and “ ·” (multiplication). The multi...
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Let k = p11p a2 2 · · ·p am m be the prime factorization of a positive integer k and let bk(n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k. If M is a positive integer, let Sk(N ;M) be the number of positive integers n ≤ N for which bk(n) ≡ 0 (mod M). If pi i ≥ √ k, we prove that, for every positive integer j lim N→∞ Sk(N ; p j i ) N = ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1984
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1984.112.237