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S = {a_i + a_j | 1 <= i, j <= 1000 with i + j \in A} is subset of A

Source: Dutch IMO TST day2 p4

August 30, 2019
Setscombinatorics

Problem Statement

Determine the number of sets A={a1,a2,...,a1000}A = \{a_1,a_2,...,a_{1000}\} of positive integers satisfying a1<a2<...<a1000≤2014a_1 < a_2 <...< a_{1000} \le 2014, for which we have that the set S={ai+aj∣1≤i,j≤1000S = \{a_i + a_j | 1 \le i, j \le 1000 with i+j∈A}i + j \in A\} is a subset of AA.
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