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
Explore with Wolfram|Alpha
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