Question

aratati ca numarul 9·(5+10+15+...+200):41 este patrat perfect.

Answer 1

$\displaystyle 9 \cdot (5+10+15+...+200):41=9 \cdot 5(1+2+3+...+40):41= \\ \\ =45(1+2+3+...+40):41=45 \cdot \frac{40(40+1)}{2} :41= \\ \\ =45 \cdot \frac{40 \cdot 41}{2} :41=45 \cdot \frac{1640}{2} :41=45 \cdot 820:41=45 \cdot 20=900=30^2$