A Pentagonal Number Sieve
نویسندگان
چکیده
منابع مشابه
A Pentagonal Number Sieve
We prove a general pentagonal sieve theorem that has corollaries such as the following First the number of pairs of partitions of n that have no parts in common is p n p n p n p n p n Second if two unlabeled rooted forests of the same number of vertices are chosen i u a r then the probability that they have no common tree is Third if f g are two monic polynomials of the same degree over the eld...
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A new expansion is given for partial sums of Euler’s pentagonal number series. As a corollary we derive an infinite family of inequalities for the partition function, p(n).
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One of the most important and widely-studied questions in computational number theory is how to efficiently compute the prime factorizations of large integers. Among other applications, fast prime-factorization algorithms would break the widely-used RSA cryptosystem, and be of great interest in complexity theory. In particular, there is no algorithm which can factor an integer n in polynomial t...
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The number field sieve is a relatively new method to factor large integers. Its most notable success is the factorization of the ninth Fermat number. It is significantly faster than all known existing integer factoring algorithms. We examine the theoretical underpinnings of the sieve; after understanding how it works, we state the algorithm. We look mostly to the algebraic number theory aspects...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1998
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2846