Question

Scrieți numărul 314^2017 ca sumă de cinci pătrate perfecte distincte.

Answer 1

Răspuns:

$314^{2017}=314\times 314^{2016}=(4+25+64+100+121)\times 314^{2016} \\ \\ =(2\times 314^{1008})^2+(5\times 314^{1008})^2+(8\times 314^{1008})^2+(10\times 314^{1008})^2+(11\times 314^{1008})^2$