1

Part of 2016 Regional Olympiad of Mexico Southeast

Problems(1)

numbers in a circle

Source: Mathematics Regional Olympiad of Mexico Southeast 2016 P1

In a circumference there are

99

natural numbers. If

a

b

are two consecutive numbers in the circle, then they must satisfies one of the following conditions:

a-b=1, a-b=2

\frac{a}{b}=2

. Prove that, in the circle exists a number multiple of

3

circlescombinatorics