Gọi \(d=ƯCLN\left(6n+5;4n+3\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}6n+5⋮d\\4n+3⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}12n+10⋮d\\12n+9⋮d\end{matrix}\right.\)
\(\Leftrightarrow1⋮d\)
\(\LeftrightarrowƯCLN\left(6n+5;4n+3\right)=1\)
\(\Leftrightarrowđpcm\)
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Gọi d=UCLN (6n+5,4n+3)
Ta có 6n+5.2=12n+10
4n+3.3=12n+9
\(\Rightarrow\)12n+10-12n+9=1
Nên 1\(⋮\)d
Nêu UCLN(6n+5,4n+3)=1
\(\Rightarrow\)dpcm
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