A cyclic system of congruences

Find all triples $(a,b,c)$ of positive integers such that the following congruences are verified:
$$\left\{\begin{array}{l} a \equiv b \pmod{c} \\ b \equiv c \pmod{a} \\ c \equiv a \pmod{b} \end{array}\right.$$where $a,b,c$ are positive integers.