Question

Aratati ca numerele N indice 1=1987+2×(1+2+3+...+1986) şi N indice 2=64+2×64+3×64+...+49×64 sunt patrate perfecte.

Answer 1

$N_1=1987+2\cdot\dfrac{1986\cdot1987}{2}=1987+1986\cdot1987=1987(1+1986)=$
$=1987\cdot1987=1987^2$

$N_2=64(1+2+3+...+49)=64\cdot\dfrac{49\cdot50}{2}=64\cdot49\cdot25=8^2\cdot7^2\cdot5^2=$

$=(8\cdot7\cdot5)^2=280^2$