(x,y,z) is a real solution to the system, then x, y and z are all positive or null because of the odd integer power 2020 in the equations. Moreover
y -x = (z +x)^2020 -(y +z)^2020 = ((z +x) -(y +z))((z +x)^2019 +(z+x)^2018 (y+z) +(z+x)^2017 (y +z)² +(z
+x)^2016 (y +z)^3... +(y +z)^2019) what is equivalent to (y -z)(1 +(z +x)^2019 +(z +x)^2018 (y +z)... +(z +x)^2 (y +z)^2018 +(y +z)^2019) = 0 where the second factor is positive. Then y = z. Also z = x. Finally a system equivalent is x = y = z = (2x)^2020…
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