Cứu em với ạ.Em cảm ơn
\(\overline{abcd}+\overline{abc}+\overline{ab}+a=8813\)
\(\Leftrightarrow1000a+100b+10c+d+\left(100a+10b+c\right)+\left(10a+b\right)+a=8813\)
\(\Leftrightarrow1111a+111b+11c+d=8813\)
- Nếu \(a\ge8\Rightarrow1111a\ge8888>8813\) (ktm)
- Nếu \(a\le6\Rightarrow1111a+111b+11c+d< 6666+999+99+9=7773< 8813\) (ktm)
\(\Rightarrow a=7\)
\(\Rightarrow7777+111b+11c+d=8813\)
\(\Rightarrow111b+11c+d=1036\)
- Nếu \(b\le8\Rightarrow111b+11c+d\le888+99+9=996< 1036\) (ktm)
\(\Rightarrow b>8\Rightarrow b=9\)
\(\Rightarrow999+11c+d=1036\Rightarrow11c+d=37\)
\(\Rightarrow11c=37-d\Rightarrow37-d\) chia hết cho 11 (1)
Mà \(0\le d\le9\Rightarrow28\le37-d\le37\) (2)
(1);(2) \(\Rightarrow37-d=33\Rightarrow d=4\)
\(\Rightarrow11c=33\Rightarrow c=3\)
Vậy \(\overline{abcd}=7934\)
