科研之友
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摘要
Let n >= 2 be an integer. Let A be a subset of [0, n] with 0, n is an element of A. Assume the greatest common divisor of all elements of A is 1. Let k be an odd integer and s = k-1/2. Then, we prove that when 3 <= k <= 11 and
vertical bar A vertical bar >= 7s + 3/ (s + 1)(7s + 4) (n - 2) + 2.
there exists a power of 2 which can be represented as a sum of k elements (not necessarily distinct) of A. But when k >= 13, the above constraint should be changed to
vertical bar A vertical bar >= s + 1/s(2) + 2s + 2 (n - 2) + 2.
In the present paper, we generalize the results of Pan and Lev, and obtain a non-trivial progress towards a conjecture of Pan.
- 出版日期2012-6
- 单位东南大学
