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numbers in a circle

Source: Mathematics Regional Olympiad of Mexico Southeast 2016 P1

October 25, 2021
circlescombinatorics

Problem Statement

In a circumference there are 9999 natural numbers. If aa and bb are two consecutive numbers in the circle, then they must satisfies one of the following conditions: a−b=1,a−b=2a-b=1, a-b=2 or ab=2\frac{a}{b}=2. Prove that, in the circle exists a number multiple of 33.
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