Question

Dau coroana si 30 de puncte! ​

Answer 1

Răspuns:

1997

Explicație pas cu pas:

Answer 2

$\it \overline{abcd}=1000a+\overline{bcd}\ \ \ \ (*)\\ \\ \overline{abcd}:\overline{bcd}=a+1\ rest\ a+2 \Rightarrow \overline{abcd}=(a+1)\overline{bcd}+a+2 \stackrel{(*)}{\Longrightarrow}\\ \\ \Rightarrow 1000a+\overline{bcd} =(a+1)\overline{bcd}+a+2|_{-\overline{bcd}} \Rightarrow 1000a=a\cdot\overline{bcd}+a+2|_{-a} \Rightarrow\\ \Rightarrow999a=a\cdot\overline{bcd}+2 \Rightarrow 999a-a\cdot\overline{bcd}=2 \Rightarrow a\cdot(999-\overline{bcd})=2 \Rightarrow$

$\it \Rightarrow \begin{cases}\it a=1,\ \overline{bcd}=997 \Rightarrow \overline{abcd}=1997\\ \\ \it a=2,\ \overline{bcd}=998 \Rightarrow \overline{abcd}=2998\end{cases}$