Let t 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 
.
, can be so written.
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.
Eric W. Weisstein. "Cauchy-Davenport Theorem."
From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Cauchy-DavenportTheorem.html
 |
|||
|
|
||
© 1999-2005 Wolfram Research, Inc.