IMO Shortlist 2014 problem N1


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May 7, 2017
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Let n \geq 2 be an integer, and let A_n be the set A_n = \{ 2^n - 2^k \, | \, k \in \mathbb{Z}, 0 \leq k < n \} \text{.} Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of A_n.

(Serbia)

Source: https://www.imo-official.org/problems/IMO2014SL.pdf