[tex]\displaystyle\bf\\\textbf{6) Se considera numarul natural}\\\\a=3^n\cdot7^{n+2}-3^{n+3}\cdot7^n\\\\\textbf{unde n este numar natutal.}\\\\\textbf{Aratati ca a este multiplu de 11.}\\\\Rezolvare\!:\\\\a=3^n\cdot7^{n}\cdot7^2-3^{n}\cdot3^3\cdot7^n\\\\a=3^n\cdot7^{n}\Big(7^2-3^3\Big)\\\\a=3^n\cdot7^{n}\Big(49-27\Big)\\\\a=3^n\cdot7^{n}\cdot22\\\\\implies ~~ a~\vdots~11~deoarece~unul~din~factori~(22)~este~multiplu~de~11.[/tex]
