Let
n
1, and let
m be an integer with
m2. We show that if a subset
A of the interval
[0,
n] satisfies that
0
A and |
A|>1+
n/2, then
mA, the set of the sum of
m (not necessarily distinct)
elements in
A, has a power of
m. This result is best
possible in the case that
m
is odd.
Mathematics Subject
Classification (2000): 11B13 - 05D05