giúp em lam bai toán trên nha

H

harrypham

[TEX]\fbox{1}[/TEX]. Chú ý [TEX]\underbrace{111...1}_{n}= \frac{10^n-1}{9}[/TEX].
Như vậy [TEX]2n+ \frac{10^n-1}{9}= \frac{18n+10^n-1}{9}[/TEX].
Nhận thấy [TEX]10 \equiv 1 \pmod{3} \Rightarrow 10^n-1 \equiv 0 \pmod{3}[/TEX].
[TEX]\Rightarrow 2n+ \frac{10^n-1}{9} \vdots 3. \ \ \ (dpcm)[/TEX].

[TEX]\fbox{2}[/TEX]. [TEX]2n+3 \vdots n-2 \Rightarrow 2(n-2)+7 \vdots n-2[/TEX]
[TEX]\Rightarrow 7 \vdots n-2 \Rightarrow n-2 \in \{ \pm 1, \pm 7\} \Rightarrow n \in \{3,1,9,-5 \}[/TEX].
 
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