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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## Details

### 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

- 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
- 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

## Related papers

## Cite this paper

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

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

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