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99 numbers around a circle

Source: AllRussian-2014, Grade 9, day1, P1

May 3, 2014
modular arithmeticnumber theory proposednumber theory

Problem Statement

On a circle there are 9999 natural numbers. If a,ba,b are any two neighbouring numbers on the circle, then a−ba-b is equal to 11 or 22 or ab=2 \frac{a}{b}=2 . Prove that there exists a natural number on the circle that is divisible by 33.
S. Berlov
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