[tex]\displaystyle{ 2^{n+1} \cdot 3^{n} + 5 \cdot 6^{n} = 2^{n} \cdot 2 \cdot 3^{n} + 5 \cdot 6^{n} }[/tex]
[tex]\displaystyle{ = 2^{n} \cdot 3^{n} \cdot 2 + 6^{n} \cdot 5 }[/tex]
[tex]\displaystyle{ =6^{n} \cdot 2 + 6^{n} \cdot 5 }[/tex]
[tex]\displaystyle{ = 6^{n} \cdot (2 + 5) }[/tex]
[tex]\displaystyle{ = 6^{n} \cdot 7 }[/tex]
ceea ce evident se divide cu7
q.e.d.
