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On the shortest weakly prime-additive numbers.
- Source :
-
Journal of Number Theory . Jan2018, Vol. 182, p258-270. 13p. - Publication Year :
- 2018
-
Abstract
- Text A positive integer n is called weakly prime-additive if n has at least two distinct prime divisors and there exist distinct prime divisors p 1 , … , p t of n and positive integers α 1 , … , α t such that n = p 1 α 1 + ⋯ + p t α t . It is clear that t ≥ 3 . In 1992, Erdős and Hegyvári proved that, for any prime p , there exist infinitely many weakly prime-additive numbers with t = 3 which are divisible by p . In this paper, we prove that, for any positive integer m , there exist infinitely many weakly prime-additive numbers with t = 3 which are divisible by m if and only if 8 ∤ m . We also present some related results and pose several problems for further research. Video For a video summary of this paper, please visit https://youtu.be/WC_VRFtY07c . [ABSTRACT FROM AUTHOR]
- Subjects :
- *INTEGERS
*PRIME numbers
*ADDITIVE functions
*DIRICHLET forms
*DIRAC equation
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 182
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 125255681
- Full Text :
- https://doi.org/10.1016/j.jnt.2017.06.013