Question

4.Aratati ca nr. a=(3 la puterea21+3 la puterea20+3 la puterea 19) impartit la 39 este patrat perfect.

Answer 1

   
[tex]\displaystyle \\ \frac{3^{21}+3^{20}+3^{19}}{39} = \\ \\ = \frac{3^{18+3}+3^{18+2}+3^{18+1}}{39} = \\ \\ = \frac{3^{18}\times 3^3+3^{18}\times 3^2+3^{18}\times 3^1}{39} = \\ \\ = \frac{3^{18}(3^3+3^2+3^1)}{39} = \\ \\ = \frac{3^{18} (27+9+3)}{39} = \frac{3^{18}\times 39}{39} = 3^{18}=3^{9 \times 2} = \boxed{(3^9)^2 = pp}[/tex]