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Cauchy-Davenport Theorem


Let t be a nonnegative integer and let x_1, ..., x_t be nonzero elements of Z_p which are not necessarily distinct. Then the number of elements of Z_p that can be written as the sum of some subset (possibly empty) of the x_i is at least min{p,t+1}. In particular, if t>=p-1, then every element of Z_p can be so written.


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References

Martin, G. "Dense Egyptian Fractions." Trans. Amer. Math. Soc. 351, 3641-3657, 1999.Vaughan, R. C. Lemma 2.14 in The Hardy-Littlewood Method, 2nd ed. Cambridge, England: Cambridge University Press, 1997.

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Cauchy-Davenport Theorem

Cite this as:

Weisstein, Eric W. "Cauchy-Davenport Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cauchy-DavenportTheorem.html

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