On an additive problem of Erdős and Straus, 1

According to Erdo{combining double acute accent}s and Straus, we define an admissible subset A of [1, N] to be such that whenever an integer can be written as a sum of s distinct elements from A, then s is well defined. Improving on previous results, we show that the cardinality of such an admissible subset A is at most (2 +o(1))√N. As shown by Straus, the constant 2 cannot be improved upon.