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Covering subsets of the integers by congruences

Volume 182 / 2018

Michael Filaseta, Wilson Harvey Acta Arithmetica 182 (2018), 43-72 MSC: Primary 11A07; Secondary 11B25. DOI: 10.4064/aa161214-4-10 Published online: 15 December 2017

Abstract

A number of results are established showing that certain subsets of the integers can be covered by congruences with distinct moduli satisfying various restrictions. For example, the primes, the powers of $2$, the Fibonacci numbers, and the sums of two squares can each be covered by congruences with distinct odd moduli $ \gt 1$.

Authors

  • Michael FilasetaDepartment of Mathematics
    University of South Carolina
    Columbia, SC 29208, U.S.A.
    e-mail
  • Wilson HarveyWalker 3-33
    University of Louisiana at Monroe
    Monroe, LA 71209, U.S.A.
    e-mail

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