[tex]\displaystyle \overline{2x3y}~\vdots~45 \Rightarrow \overline{2x3y} ~\vdots~5~si~\overline{2x3y} ~\vdots~9.~(deoarece~(5,9)=1) \\ \\ \overline{2x3y} ~\vdots~5 \Rightarrow y \in \{ 0, 5 \}. \\ \\ \overline{2x3y} ~\vdots~9 \Rightarrow 2+x+3+y=5+x+y~\vdots~9. \\ \\ Cazul~1:~y=0 \Rightarrow 5+x+y=5+x~\vdots~9 \Rightarrow x=4.~Am~gasit~ \\ \\ numarul~2430. \\ \\ Cazul~2:~y=5 \Rightarrow 5+x+y=10+x~\vdots~9 \Rightarrow x=8.~Am~gasit \\ \\ numarul~2835. \\ \\ Numerele~cautate~sunt~2430~si~2835.[/tex]
