Gọi `d` là `ƯCLN(14n+3;21n+4)`
Ta có :
$\left\{{}\begin{matrix}21n+4⋮d\\14n+3⋮d\end{matrix}\right.$
$⇔\left\{{}\begin{matrix}2\left(21n+4\right)⋮d\\3\left(14n+3\right)⋮d\end{matrix}\right.$
$⇔\left\{{}\begin{matrix}42n+8⋮d\\42n+9⋮d\end{matrix}\right.$
$⇔\left(42n+9\right)-\left(42n+8\right)⋮d$
`⇔ 1\vdotsd`
`⇔ d=1`
`⇔ ƯCLN(14n+3;21n+4)=1`
Xin hay nhất !
