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
On a Problem of Erdős
✍ Scribed by Csaba Sándor
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 236 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
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.
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