S:E18.128

S:E18.128 (Vasile Ienuțaș)

Scrieți numărul $2018^{2017}$ ca sumă de patru pătrate perfecte nenule distincte.

Soluție.

Din 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 = 3^2+4^2+12^2+43^2} se obține

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

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