Find all positive integers $\overline{xyz}$ ($x$, $y$ and $z$ are digits) such that $\overline{xyz} = x+y+z+xy+yz+zx+xyz$
Problem
Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2017
Tags: Digits, number theory
Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2017
Tags: Digits, number theory
Find all positive integers $\overline{xyz}$ ($x$, $y$ and $z$ are digits) such that $\overline{xyz} = x+y+z+xy+yz+zx+xyz$