4

Part of 2021 Austrian MO Regional Competition

Problems(1)

x | (y + 1), y | (z + 1) and z | (x + 1)

Source: 2021 Austrian Regional Competition For Advanced Students p4

Determine all triples

(x, y, z)

of positive integers satisfying

x | (y + 1)

y | (z + 1)

z | (x + 1)

.
(Walther Janous)

number theorydividesdivisible