PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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


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$.


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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image