MathDB

Problem 6 of Fourth round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018

number theory

Problem Statement

Find all sets

(a, b, c)

of different positive integers

a

b

c

, for which:
*

2a - 1

is a multiple of

b

;
*

2b - 1

is a multiple of

c

;
*

2c - 1

is a multiple of

a