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combo NT with 108 pos. integers <= 2015

Source: China Northern MO 2015 grade 11 p4 CNMO

May 5, 2024
combinatoricsnumber theory

Problem Statement

It is known that a1,a2,...a108a_1, a_2,...a_{108} are 108108 different positive integers not exceeding 20152015. Prove that there is a positive integer kk such that there are at least four different pairs (i,j)(i, j) satisfying ai−aj=ka_i-a_j =k.
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