Ta có: \(\hept{\begin{cases}x:13\text{ }dư\text{ }1\\x:15\text{ }dư\text{ }1\\x:61\text{ }dư\text{ }1\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x-1⋮13\\x-1⋮15\\x-1⋮61\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x-1\inƯ\left(13\right)\\x-1\inƯ\left(15\right)\\x-1\inƯ\left(61\right)\end{cases}}\)
\(\Rightarrow x-1\inƯC\left(13,15,61\right)=\left\{1\right\}\)
\(\Rightarrow x-1=1\)
\(\Leftrightarrow x=2\)
Vậy \(x=2\)thỏa mãn đề.
Ta có: \(\hept{\begin{cases}x:13\text{ }dư\text{ }1\\x:15\text{ }dư\text{ }1\\x:61\text{ }dư\text{ }1\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x-1⋮13\\x-1⋮15\\x-1⋮61\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x-1\in B\left(13\right)\\x-1\in B\left(15\right)\\x-1\in B\left(61\right)\end{cases}}\)
\(\Rightarrow x-1\in BC\left(13,15,61\right)=\left\{0;11895;23790;...\right\}\)
\(\Rightarrow x\in\left\{1;11896;23791;...\right\}\)
Vậy \(x\in\left\{1;11896;23791;...\right\}\)thỏa mãn đề.
