We study sets P of k primes that satisfy the condition gcd(> A&> B, > P)=1 whenever A and B are disjoint non-empty subsets of P. It is known that such sets of primes exist for all positive integers k. It is of interest to know the asymptotic behavior of n k , the smallest natural number that is the
Prime and prime power divisibility of Catalan numbers
โ Scribed by Ronald Alter; K.K Kubota
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 549 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For each positive integer j , let ฮฒ j (n) := p|n p j . Given a fixed positive integer k, we show that there are infinitely many positive integers n having at least two distinct prime factors and such that ฮฒ j (n) | n for each j โ {1, 2, . . . , k}.
## Abstract In this paper we either prove the nonโexistence or give explicit construction of primitive symmetric (__v, k__, __ฮป__) designs with __v__=__p__^__m__^<2500, __p__ prime and __m__>1. The method of design construction is based on an automorphism group action; nonโexistence results additio
We prove a version of Hensel's Lemma which applies to analytic functions on the \(p\)-adic integers. This is used to obtain results on the divisibility of Stirling numbers of the second kind which generalise results of Davis, 1995 Academic Press. lnc
The paper classifies (up to isomorphism) those groups of prime power order whose derived subgroups have prime order.