5

Part of 2018 Auckland Mathematical Olympiad

Problems(2)

(a+1)/b , (b+1)/c , (a+1)/b are integers (2018 Auckland MO J5)

Source:

Find all possible triples of positive integers,

a, b, c

\frac{a+1}{b}

\frac{b+1}{c}

\frac{c+1}{a}

are also integers.

number theoryIntegers

sequence of numbers +1 and -1 of length n (2018 Auckland MO S5)

Source:

There is a sequence of numbers

+1

-1

n

. It is known that the sum of every

10

neighbouring numbers in the sequence is

0

and that the sum of every

12

neighbouring numbers in the sequence is not zero. What is the maximal value of

n