1, \(\overline{a45b}\) \(⋮\) 2; 3; 5; 9
⇒ b = 0; a + 4 + 5 + b ⋮ 9 ⇒ a + 9 ⋮ 9 ⇒ a = 9
Vậy \(\overline{a45b}\) = 9450
2, \(\overline{a1b8}\) \(⋮\) 2;3;9 ⇔ a + 1 + b + 8 ⋮ 9 ⇒ a + b ⋮ 9
⇒ b = 0; 1; 2; 3; 4; 5; 6; 7; 8
a = 9; 8; 7; 6; 5; 4; 3; 2; 1
\(\Rightarrow\) \(\overline{a1b8}\) = 9108; 8118; 7128; 6138; 5148; 4158; 3168; 2178; 1188
3, 2025 + \(\overline{a36}\) \(⋮\) 3
⇔ 2 + 0 + 2 + 5 + a + 3 + 6 ⋮ 3
18 + a ⋮ 3
a ⋮ 3
a = 0; 3; 6; 9
4, 125 + 5100 + \(\overline{31a}\) ⋮ 5
⇔ \(\overline{31a}\) ⋮ 5
a ⋮ 5
a = 0; 5
1) \(\overline{x45y}⋮2;3;5;9\)
\(\Rightarrow y=0\left(⋮2;5\right)\)
\(x+4+5+0⋮\left(3;9\right)\)
\(\Rightarrow x=9\)
\(\Rightarrow\overline{x45y}=9450\)
3) \(2025+\overline{x36}⋮3\)
mà \(2025⋮3\)
\(\Rightarrow\overline{x36}⋮3\)
\(\Rightarrow x+3+6⋮3\)
\(\Rightarrow x\in\left\{3;6;9\right\}\)
3) \(2022^{10}+4^{20}+\overline{53x}⋮2\)
\(2022^{10}=2022^8.2022^2=\overline{.....6}x\overline{....4}=\overline{.....4}⋮2\)
\(4^{20}=\overline{.....6}⋮2\)
\(\Rightarrow\overline{53x}⋮2\)
\(\Rightarrow x\in\left\{0;2;4;6;8\right\}\)
5, 202210 + 420 + \(\overline{53a}\) ⋮ 2
⇔ \(\overline{53a}\) ⋮ 2
a = 0; 2; 4; 6; 8
6, \(\overline{37a}\) + \(\overline{b23}\) ⋮ 3
⇔ 3 + 7 + a + b + 2 + 3 ⋮ 3
15 + a + b ⋮ 3
a + b \(⋮\) 3
a + b = 3; 6; 9; 12; 15; 18
a + b = 3 ⇒ b =0; 1; 2 a = 3; 2; 1
a + b = 6 ⇒ b = 0; 1; 2; 3; 4; 5 a = 6; 5; 4; 3; 2; 1
a + b = 9 ⇒ b = 0; 1; 2; 3; 4;5;6;7;8 a = 9;8;7;6;5;4;3;2;1
a + b = 12 ⇒ b = 3; 4; 5; 6; 7; 8; 9 a = 9;8;7;6;5;4;3
a + b = 15; b = 6; 7; 8; 9 a = 9; 8; 7; 6
a + b = 18; a = 9; b = 9
