[tex] \it \overline{51xy}\ \vdots\ 45 \Rightarrow \begin{cases}\it \overline{51xy}\ \vdots\ 5 \Rightarrow y\in\{0,\ 5\}\ \ \ \ \ (1)
\\ \\
\it\overline{51xy}\ \vdots\ 9\ \ \ \ \ (2) \end{cases} [/tex]
[tex] \it (1),\ (2) \Rightarrow \overline{51x0}\ \vdots\ 9 \ \ sau \ \ \overline{51x5}\ \vdots\ 9
\\ \\ \overline{51x0}\ \vdots\ 9\Rightarrow (5+1+x+0)\ \vdots\ 9 \Rightarrow (6+x)\ \vdots\ 9\Rightarrow x=3\Rightarrow\ n = 5130
\\ \\ \overline{51x5}\ \vdots\ 9\Rightarrow (5+1+x+5)\ \vdots\ 9 \Rightarrow (11+x)\ \vdots\ 9\Rightarrow x=7\Rightarrow\ n = 5175 [/tex]
Cel mai mic număr care corespunde condiției din enunț este 5130.
