Research PapersNo Access

Two questions concerning covering systems

Joshua Harrington

Department of Mathematics, Cedar Crest College, 100 College Drive, Allentown, PA 18104, USA

https://doi.org/10.1142/S179304211550075XCited by:2 (Source: Crossref)

Abstract

Ever since Erdős introduced the concept of a covering system in 1950, many questions have arisen regarding the existence of certain types of covering systems. Two of the most famous questions regarding covering systems are the odd covering problem and the minimum modulus problem. In the current paper, we ask two questions that are related to these famous questions and provide results for each.

Keywords:

AMSC: 11A07, 11B25

References

A. Brunneret al., Generalizing Sierpiński numbers to base b, New Aspects of Analytic Number Theory, Proceedings of RIMS, Surikaisekikenkyusho Kokyuroku (Kyoto University, Kyoto, 2009) pp. 69–79. Google Scholar
Y. G. Chen , J. Number Theory 89 , 121 ( 2001 ) . Crossref, Web of Science, Google Scholar
P. Erdős , Summa Brasil. Math. 2 , 113 ( 1950 ) . Google Scholar
M. Filaseta , K. Ford and S. Konyagin , Illinois J. Math. 44 , 633 ( 2000 ) . Crossref, Web of Science, Google Scholar
M. Filaseta and J. Harrington, Acta. Arith. 155(2), 149 (2012). Crossref, Web of Science, Google Scholar
M. Filasetaet al., J. Comb. Number Theory 2(1), 25 (2010). Google Scholar
M. Filaseta and M. Mossinghoff, Math. Comp. 81(279), 1571 (2012). Crossref, Web of Science, Google Scholar
S. Guo and Z. W. Sun, Adv. Appl. Math. 35(2), 182 (2005). Crossref, Web of Science, Google Scholar
R. K. Guy , Unsolved Problems in Number Theorem , 3rd edn. ( Springer , New York , 1994 ) . Crossref, Google Scholar
B. Hough, Ann. Math. 181(1), 361 (2015). Crossref, Web of Science, Google Scholar
L. Jones and D. White, J. Integer Seq. 14(5), 12 (2001). Google Scholar
C. E. Krukenberg, Covering sets of the integers, Ph.D. thesis, University of Illinois at Urbana-Champaign (1971) . Google Scholar
P. Nielsen , J. Number Theory 129 , 640 ( 2008 ) . Crossref, Web of Science, Google Scholar
H. Riesel , Elementa 39 , 258 ( 1956 ) . Google Scholar
A. Schinzel , Acta Arith. 13 , 91 ( 1967 ) . Crossref, Google Scholar
W. Sierpiński , Elem. Math. 15 , 73 ( 1960 ) . Google Scholar
Z. W. Sun, Acta Arith. 72(2), 109 (1995). Crossref, Web of Science, Google Scholar
K. Zsigmondy , Monatsch. Math. Phys. 3 , 265 ( 1892 ) . Crossref, Google Scholar