Question

$scrie \: {2017}^{2017} ca \: suma \: de \: doua \: patrate \: perfecte$

Answer 1

  $\displaystyle\bf\\2017^{2017}=2017^{2016+1}=2017^{2016}\times2017^1=2017^{2016}\times2017\\\\\text{Descompunem numarul 2017 in suma de 2 patrate perfecte}\\\\2017=1936+81 = 44^2 + 9^2\\\\2017^{2016}\times2017=2017^{2016}(1936+81)=\\\\=2017^{1008\times2}(44^2+9^2)=\Big(2017^{1008}\Big)^2\Big(44^2+9^2\Big)=\\\\=\Big(2017^{1008}\Big)^2\times44^2+ \Big(2017^{1008}\Big)^2\times9^2=\\\\=\boxed{\bf\Big(2017^{1008}\times44\Big)^2+\Big(2017^{1008}\times9\Big)^2}~~=\text{ suma de 2 patrate perfecte.}$

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