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a,b, a+b, a-b incudes in 2003 pos. int. - All-Russian MO 2003 Regional (R4) 8.8

Source:

September 17, 2024
number theory

Problem Statement

A set of 20032003 positive numbers is such that for any two numbers aa and bb included in it (a>ba > b) at least one of the numbers a+ba + b or aāˆ’ba - b also included in the set. Prove that if these numbers are ordered by increasing, then the differences between adjacent numbers will be the same.