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Prove that there exist fewer than 2^m such positive integers

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September 15, 2010
number theoryAdditive Number TheoryAdditive combinatoricssystem of equationsIMO ShortlistIMO Longlist

Problem Statement

Let mm positive integers a1,…,ama_1, \dots , a_m be given. Prove that there exist fewer than 2m2^m positive integers b1,…,bnb_1, \dots , b_n such that all sums of distinct bkb_k’s are distinct and all ai (i≤m)a_i \ (i \leq m) occur among them.
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