Salut.
[tex]\displaystyle{x=4^{n}\times3^{2n+1}+2^{2n+3}\times9^{n} }[/tex]
- Descompunem expresia în factori.
[tex]\displaystyle{x=2^{2n} \times 3^{2n+1}+2^{2n+3}\times3^{2n} }[/tex]
[tex]\displaystyle{x=(3 +2^{3})\times2^{2n}\times3^{2n} }[/tex]
[tex]\displaystyle{x=(3+8)\times2^{2n}\times3^{2n} }[/tex]
[tex]\displaystyle{x=11\times2^{2n}\times3^{2n} }[/tex]
[tex]\displaystyle{x=11\times6^{2n} }[/tex]
[tex]\displaystyle{x=11\times36^{n} }[/tex]
=> [tex]\displaystyle{x}[/tex] se divide cu 11
=> adevărat
- Lumberjack25
