a. Gọi \(d=ƯCLN\left(12n+1;30n+2\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}12n+1⋮d\\30n+2⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}60n+5⋮d\\60n+4⋮d\end{matrix}\right.\)
\(\Leftrightarrow1⋮d\)
Vì \(d\in N;1⋮d\Leftrightarrow d=1\)
\(\LeftrightarrowƯCLN\left(12n+1;30n+2\right)=1\)
Vậy .........
b. Gọi \(d=ƯCLN\left(14n+17;21n+25\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}14n+17⋮d\\21n+25⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}42n+51⋮d\\42n+50⋮d\end{matrix}\right.\)
\(\Leftrightarrow1⋮d\)
Vì \(d\in N;1⋮d\Leftrightarrow d=1\)
\(\LeftrightarrowƯCLN\left(14n+17;21n+25\right)=1\)
Vậy ...
Gọi \(d\) là \(UCLN\left(12n+1;30n+2\right)\)
\(\Rightarrow\left\{{}\begin{matrix}12n+1⋮d\\30n+2⋮d\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}60n+5⋮d\\60n+4⋮d\end{matrix}\right.\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
Vậy p/s \(A\) tối giản với mọi \(n\in N\)
b) Gọi \(d\) là \(UCLN\left(14n+17;21n+25\right)\)
\(\Rightarrow\left\{{}\begin{matrix}14n+17⋮d\\21n+25⋮d\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}42n+51⋮d\\42n+50⋮d\end{matrix}\right.\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
Vậy p/s \(B\) tối giản với mọi \(n\in N\)
