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On a conjecture of Erdős, Graham and Spencer
- Source :
-
Journal of Number Theory . Aug2006, Vol. 119 Issue 2, p307-314. 8p. - Publication Year :
- 2006
-
Abstract
- Abstract: It is conjectured by Erdős, Graham and Spencer that if with , then this sum can be decomposed into n parts so that all partial sums are ⩽1. This is not true for as shown by , , . In 1997, Sándor proved that Erdős–Graham–Spencer conjecture is true for . In this paper, we reduce Erdős–Graham–Spencer conjecture to finite calculations and prove that Erdős–Graham–Spencer conjecture is true for . Furthermore, it is proved that Erdős–Graham–Spencer conjecture is true if and no partial sum (certainly not a single term) is the inverse of an positive integer. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 119
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 21683478
- Full Text :
- https://doi.org/10.1016/j.jnt.2005.11.003