MathDB

N1

Part of 2014 IMO Shortlist

Problems(1)

IMO Shortlist 2014 N1

Source:

7/11/2015
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
IMO Shortlistnumber theoryFrobeniusAdditive combinatoricsAdditive Number Theoryadditive representationinduction