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Sum and Sets of Integers

Source: SMO(O) 2014 #4

January 22, 2015
graph theorycombinatorics

Problem Statement

Let FF be a finite non-empty set of integers and let nn be a positive integer. Suppose that
∙\bullet Any x∈Fx \in F may be written as x=y+zx=y+z for some yy, z∈Fz \in F; ∙\bullet If 1≤k≤n1 \leq k \leq n and x1x_1, ..., xk∈Fx_k \in F, then x1+⋯+xk≠0x_1+\cdots+x_k \neq 0.
Show that FF has at least 2n+22n+2 elements.
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