On a conjecture of Crittenden and Vanden Eynden concerning coverings by arithmetic progressions

Autor:	R. J. Simpson
Rok vydání:	1997
Předmět:	Discrete mathematics Conjecture Implicit function General Medicine Arithmetic Value (mathematics) Mathematics Counterexample
Zdroj:	Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics. 63:396-420
ISSN:	0263-6115
Popis:	Crittenden and Vanden Eynden conjectured that ifnarithmetic progressions, each having modulus at leastk, include all the integers from 1 tok2n-k+1, then they include all the integers. They proved this for the casesk= 1 andk= 2. We give various necessary conditions for a counterexample to the conjecture; in particular we show that if a counterexample exists for some value ofk, then one exists for thatkand a value ofnless than an explicit function ofk.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3790ca6fee9806265807e08b90a3e9e7 https://doi.org/10.1017/s1446788700000975 Zobrazit plný text záznamu