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Numbers on circle

Source: St Petersburg Olympiad 2012, Grade 10, P4

September 29, 2017
number theory

Problem Statement

Some notzero reals numbers are placed around circle. For every two neighbour numbers a,ba,b it true, that a+ba+b and 1a+1b\frac{1}{a}+\frac{1}{b} are integer. Prove that there are not more than 44 different numbers.
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