Question

Aratati ca numarul a=(3 la 21 + 3 la 20 +3 la 19):39 este patrat perfect ..

Answer 1

$a= (3^{19}+3^{20}+3^{21}):39 \\ a=3^{19}(1+3+3^{2}):39 \\ a=3^{19}*13:39 \\ a=3^{19}* \frac{1}{3} \\ a= \frac{3^{19}}{3} \\a=3^{18}=(3^{9})^{2}$