Question

Answer 1

\(x^3+y^3=14z^3-91t^3\)

\(\Rightarrow x^3+y^3+z^3+t^3=15z^3-90t^3\)

\(\Rightarrow x^3+y^3+z^3+t^3=3\left(5z^3-30t^3\right)\)

\(\Rightarrow\left(x^3+y^3+z^3+t^3\right)⋮3\) (1)

Mặt khác ta có:

\(x^3\equiv x\left(\mod3\right)\); \(y^3\equiv y\left(\mod3\right)\) ; \(z^3\equiv z\left(\mod3\right)\); \(t^3\equiv t\left(\mod3\right)\)

\(\Rightarrow x^3+y^3+z^3+t^3\equiv x+y+z+t\left(\mod3\right)\) (2)

(1);(2) \(\Rightarrow\left(x+y+z+t\right)⋮3\)