MathDB
IMO Shortlist 2014 N1

Source:

July 11, 2015
IMO Shortlistnumber theoryFrobeniusAdditive combinatoricsAdditive Number Theoryadditive representationinduction

Problem Statement

Let n≥2n \ge 2 be an integer, and let AnA_n be the set An={2n−2k∣k∈Z, 0≤k<n}.A_n = \{2^n - 2^k\mid k \in \mathbb{Z},\, 0 \le k < n\}. Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of AnA_n .
Proposed by Serbia
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