[tex]\\ \\ Observam \\ 3^{4n+1} = 3 * 3^{4n} = 3 * 9^{2n} \\ \\ Obtinem \\ \\ 9^{2n+1} + 3 * 9^{2n} + 1 = 8^{2n+1} + 8^{2n} \\ \\ Observam \\ \\ 9^{2n+1} \ \textgreater \ 8^{2n+1} \\ \\ 9^{2n} \ \textgreater \ 8^{2n} \\ \\[/tex]
Pentru orice n∈N*,
Deci
[tex]9^{2n+1} + 3^{4n+1} + 1 \ \textgreater \ 8^{2n+1} + 8^{2n} \\[/tex]
