A note on sumsets and difference sets in ℤ/n

Christopher J. Richardson and Craig V. Spencer
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 18, 2012, Number 3, Pages 45—47
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Authors and affiliations

Christopher J. Richardson
Department of Math, Physics, and Computer Science, Baker University
P.O. Box 65, Baldwin City, KS 66006, United States

Craig V. Spencer
Department of Mathematics, Kansas State University
138 Cardwell Hall, Manhattan, KS 66506, United States

Abstract

In this brief note, we investigate the quantity k(n), which is the smallest natural number r such that for all subsets A  ℤ/nℤ satisfying A ⊆ A = ℤ/nℤ, we have rA = ℤ/nℤ.

Keywords

  • Sumsets
  • Difference sets

AMS Classification

  • 11B30
  • 11B13
  • 05B10

References

  1. Problem Session of the Conference in Number Theory, Carleton University, June 28, 2011, http://www.fields.utoronto.ca/programs/scientific/10-11/numtheoryconf/conferenceproblems.pdf
  2. Granville, A. An introduction to additive combinatorics, Additive Combinatorics (Providence, RI, USA), CRM Proceedings and Lecture Notes, American Math. Soc., Vol. 43, 2007, 1–27

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Cite this paper

APA

Richardson C. J., & Spencer C. V. (2012). A note on sumsets and difference sets in ℤ/nℤ, Notes on Number Theory and Discrete Mathematics, 18(3), 45-47.

Chicago

Richardson C. J., and Craig V. Spencer. “A Note on Sumsets and Difference Sets in ℤ/nℤ.” Notes on Number Theory and Discrete Mathematics 18, no. 3 (2012): 45-47.

MLA

Richardson C. J., and Craig V. Spencer. “A Note on Sumsets and Difference Sets in ℤ/nℤ.” Notes on Number Theory and Discrete Mathematics 18.3 (2012): 45-47. Print.

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