Đặt A=5^{n} \cdot\left(5^{n}+1\right)-6^{n} \cdot\left(3^{n} + 2^n\right)
\Rightarrow A=\left(25^{n}-18^{n}\right)-\left(12^{n}-5^{n}\right)
Ta có:
\left\{\begin{array}{c}25^{n}-18^{n} \vdots (25-18) \\12^{n}-5^{n} \vdots (12-5)\end{array} \Leftrightarrow A \vdots 7\right.
Ta lại có...