Let be a nonnegative integer and let , ..., be nonzero elements of which are not necessarily distinct. Then the number of elements of that can be written as the sum of some subset (possibly empty) of the is at least . In particular, if , then every element of can be so written.
Cauchy-Davenport Theorem
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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.Referenced on Wolfram|Alpha
Cauchy-Davenport TheoremCite this as:
Weisstein, Eric W. "Cauchy-Davenport Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cauchy-DavenportTheorem.html