\(Gọi:d=\left(a,b\right)\Rightarrow\left\{{}\begin{matrix}a=da`\\b=db`\end{matrix}\right.với:\left(a`,b`\right)=1và:a`>b`\)
\(Taco:ab=\left(a,b\right).\left[a,b\right]\Rightarrow a`b`d^2=d.\left[a,b\right]\Rightarrow\left[a,b\right]=a`b`d\)
\(\left(a,b\right)+\left[a,b\right]=d+a`b`d=d\left(1+a`b`\right)=14\Rightarrow d\inƯ\left(14\right)\Rightarrow d\in\left\{1;2;7;14\right\}\)
\(+,d=1\Rightarrow a`b`+1=14\Rightarrow a`b`=13.Mà\left(a`,b`\right)=1va:a`>b`\Rightarrow\left\{{}\begin{matrix}a`=13\\b`=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=13\\b=1\end{matrix}\right.\)
\(+,d=2\Rightarrow a`b`+1=7\Rightarrow a`b`=6Mà\left(a`,b`\right)=1va:a`>b`\Rightarrow\left\{{}\begin{matrix}a`=3\\b`=2\end{matrix}\right.hoặc:\left\{{}\begin{matrix}a`=6\\b`=1\end{matrix}\right.\Rightarrow\left(a,b\right)\in\left\{\left(6;4\right),\left(12;2\right)\right\}\)
\(+,d=7\Rightarrow a`b`+1=2\Rightarrow a`b`=1\left(loại\right)\)
\(+,d=14\Rightarrow a`b`+1=1\Rightarrow a`b`=0\left(loại\right)\)
\(Vậy:\left(a,b\right)\in\left\{\left(13;1\right),\left(12;2\right),\left(6;4\right)\right\}\)
