Three-Variable Homogeneous Cubic

Algebra Level 5

x,y x, y and zz are integers such that 10x,y,z10 -10 \leq x, y, z \leq 10 . How many ordered triplets (x,y,z) (x, y, z) satisfy x3+y3+z3=3xyzx^3+y^3+z^3 = 3 xyz ?

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