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Covering intervals with arithmetic progressions


In this short note we give a simple proof of a 1962 conjecture of Erdős, first proved in 1969 by Crittenden and Vanden Eynden, and note two corollaries.

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Corresponding author

Correspondence to R. Morris.

Additional information

The first two authors were partially supported by NSF grant DMS 1600742.

The third author was partially supported by CNPq (Proc. 303275/2013-8) and FAPERJ (Proc. 201.598/2014).

The fifth author was supported by a Trinity Hall Research Studentship.

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Balister, P., Bollobás, B., Morris, R. et al. Covering intervals with arithmetic progressions. Acta Math. Hungar. 161, 197–200 (2020).

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Key words and phrases

  • covering system
  • arithmetic progression

Mathematics Subject Classification

  • 11A07
  • 11B25