(1) Bureau of Human Resources National Personnel Authority, 1-2-3 Kasumigaseki, Chiyoda-ku, Tokyo, 100-8913, Japan
Abstract:
Let n1, and letm be an integer withm2. We show that if a subsetA of the interval[0,n] satisfies that0A and |A|>1+n/2, then mA, the set of the sum ofm (not necessarily distinct)elements in A, has a power ofm. This result is bestpossible in the case that mis odd.
1, and letm be an integer withm
A and |A|>1+n/2, then mA, the set of the sum ofm (not necessarily distinct)elements in A, has a power ofm. This result is bestpossible in the case that mis odd.