𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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.


📜 SIMILAR VOLUMES


On a Problem of Erdős and Sárközy
✍ Tomasz Schoen 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 89 KB

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 Erdös in Additive Number
✍ Dieter Wolke 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 263 KB

In 1954 Lorentz and Erdo s showed that there are very thin sets of positive integers complementary to the set of primes. In particular, there is an A N with (ii) every n n 0 can be written as n=a+ p, a # A, p prime. Erdo s conjectured that the bound (i) could be sharpened to o(ln 2 x) or even O(ln

On A Problem of Erdős and Turán and Some
✍ N. Alon; M.N. Kolountzakis 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 315 KB

We employ the probabilistic method to prove a stronger version of a result of Helm, related to a conjecture of Erdos and Turan about additive bases of the positive integers. We show that for a class of random sequences of positive integers \(A\), which satisfy \(|A \cap[1, x]| \gg \sqrt{x}\) with pr

On an anti-Ramsey problem of Burr, Erdős
✍ Gábor N. Sárközy; Stanley Selkow 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 98 KB

## Abstract Given a graph __L__, in this article we investigate the anti‐Ramsey number χ~__S__~(n,e,L), defined to be the minimum number of colors needed to edge‐color some graph __G__(__n__,__e__) with __n__ vertices and __e__ edges so that in every copy of __L__ in __G__ all edges have different

A Minimax Problem Admitting the Equiosci
✍ Ying Guang Shi 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 190 KB

This paper shows that under certain conditions a solution of the minimax problem min a<x 1 < } } } <x n <b max 1 i n+1 f i (x 1 , ..., x n ) admits the equioscillation characterizations of Bernstein and Erdo s and has strong uniqueness. This problem includes as a particular example the optimal Lagra

Cameron-Erdős Modulo a Prime
✍ Vsevolod F Lev; Tomasz Schoen 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 315 KB

We prove that for p prime and su$ciently large, the number of subset of 9 N free of solutions of the equation x#y"z (that is, free of Schur triples) satis"es ]"42N\CN, where and are positive absolute constants.