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

Source: 2021 Austrian Regional Competition For Advanced Students p4

May 31, 2021

number theorydividesdivisible

Problem Statement

Determine all triples

(x, y, z)

of positive integers satisfying

x | (y + 1)

y | (z + 1)

and

z | (x + 1)

.
(Walther Janous)