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among d_1=x_2-x_1, d_2=x_3-x_2, ..., d_{101}=x_{102}-x_{101}, 26 are equal

Source: Greece JBMO TST 2008 p3

April 29, 2019
combinatoricsIntegersDifference

Problem Statement

Let x1,x2,x3,...,x102x_1,x_2,x_3,...,x_{102} be natural numbers such that x1<x2<x3<...<x102<255x_1<x_2<x_3<...<x_{102}<255. Prove that among the numbers d1=x2−x1,d2=x3−x2,...,d101=x102−x101d_1=x_2-x_1, d_2=x_3-x_2, ..., d_{101}=x_{102}-x_{101} there are at least 2626 equal.
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