Question

Aratati ca numarul a=(3^21+3^20+3^19)/39 este patrat perfect

Answer 1

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

deci este un patrat perfect