[tex]\it \dfrac{\overline{ab}}{a}=\dfrac{10a+b}{a}=\dfrac{10a}{a}+\dfrac{b}{a}=10+\dfrac{b}{a}\in\mathbb{N} \Rightarrow a|b\ \ \ \ (1)\\ \\ Analog,\ rezult\breve{a}:\\ \\ b|c\ \ \ \ (2)\\ \\ c|a\ \ \ \ (3)\\ \\ (1),\ (2) \Rightarrow a|c\ \ \ \ (4)\\ \\ (3),\ (4) \Rightarrow a=c\ \ \ \ (5)[/tex]
[tex]\it (1),\ (2),\ (5) \Rightarrow a|b\ \ si\ \ b|a \Rightarrow a=b\ \ \ \ (6)\\ \\ \\ (5),\ (6) \Rightarrow \overline{abc} \in \{111,\ 222,\ 333,\ ...\ 999\}[/tex]
