On a problem of Erdős, Herzog and Schönheim
✍ Scribed by Yong-Gao Chen; Cui-Ying Hu
- Book ID
- 113564797
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 212 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Theorem 1. For every n 2 there exist integers 1<a 1 <a 2 < } } } <a s such that s i=1 1Âa i <n and this sum cannot be split into n parts so that all partial sums are 1.
Let A=[a 1 , a 2 , ...] N and put A(n)= a i n 1. We say that A is a P-set if no element a i divides the sum of two larger elements. It is proved that for every P-set A with pairwise co-prime elements the inequality A(n)<2n 2Â3 holds for infinitely many n # N. ## 2001 Academic Press where A(n)= a i
Let D be a planar cyclic difference set with 0 ∈ D. Krasikov and Schönheim proposed in the problem: prove that there are elements d i , d j , d k ∈ D -{0} such that d i + d j + d k = 0. We prove this and a little more.