Đặt \(\overline{abcd}=m^2\left(m\inℕ^∗\right)\)
Ta có: \(m^2⋮33\Rightarrow m^2⋮3;11\)
\(\Rightarrow m^2⋮9;121\)
Vì (9;121) =1 nên m2 chia hết cho 9.121
=> m2 chia hết cho 1089
=> m2= 1089k2 \(\left(k\inℕ^∗\right)\)
Vì \(1000\le m^2\le9999\Rightarrow1000\le1089k^2\le9999\)
\(\Rightarrow1\le k^2\le9\Rightarrow k^2\in\left\{1;4;9\right\}\)\(\Rightarrow m^2\in\left\{1089;4356;9801\right\}\)
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