Question

Aratati ca ca numărul a=3 la puterea n+2 + 3 la puterea n se divide cu 30, oricare ar fi n cuprins in N(multimea numerelor naturale)

Answer 1

[tex]a=3^{n+2}+3^{n}\\a=3^{n}*3^{2}+3^{n}*3^{0}\\a=3^{n}*(3^{2}+3^{0})\\ a=3^n}*(9+1)\\a=3^{n}*10\\3^{n}=M_3\\10=M_1_0\\M_3*M_1_0=M_3_0[/tex]