Question

1. Aratati ca numarul $3^{45} + 3^{44} + 3^{40}$ se imparte exact la 13.
2. Determinati cel mai mare si cel mai mic nuamr natural de trei cifre care impartit la 12 da de fiecare data restul 10.

Answer 1

[tex]1)3^{45}+3^{44}+3^{40}=3^{40}(3^5+3^4+1) =3^{40}\cdot325\\ 3^{40}\cdot325:13=3^{40}\cdot25\\ 2)\overline{abc}:12=\ q\ rest\ 10\\ \overline{abc}=12q\ rest\ 10\\ q=8=>\overline{abc}=106\\ q=82=>\overline{abc}=994[/tex]