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Covering intervals with arithmetic progressions

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Abstract

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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References

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    P. Balister & B. Bollobás

  2. Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom

    B. Bollobás & M. Tiba

  3. IMPA, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, 22460-320, Brazil

    R. Morris & J. Sahasrabudhe

  4. University of Cambridge, Trumpington Street, Peterhouse, CB2 1RD, United Kingdom

    J. Sahasrabudhe

Authors
  1. P. Balister
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  2. B. Bollobás
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  3. R. Morris
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  4. J. Sahasrabudhe
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  5. M. Tiba
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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). https://doi.org/10.1007/s10474-019-00980-z

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  • DOI: https://doi.org/10.1007/s10474-019-00980-z

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