S:E18.128

S:E18.128 (Vasile Ienuțaș)

Scrieți numărul Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2018^{2017}} ca sumă de patru pătrate perfecte nenule distincte.

Soluție.

Din $2018=3^{2}+4^{2}+12^{2}+43^{2}$ se obține

$$2018^{2017}=2018\cdot 2018^{2016}=\left(3^{2}+4^{2}+12^{2}+43^{2}\right)\cdot \left(2018^{1008}\right)^{2}$$

Deci

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2018^{2017} = \left( 3 \cdot 2018^{1008}\right)^2 + \left( 4 \cdot 2018^{1008}\right)^2 + \left( 12 \cdot 2018^{1008}\right)^2 + \left( 43 \cdot 2018^{1008}\right)^2}