Fermat's Last Theorem

Andrew Wiles, pictured above, was recently awarded the 2016 Abel Prize for his 1994 proof of Fermat's last theorem.

Suppose n=2016n=2016 and x,y,z|x|,|y|,|z| are all less than 10. How many solutions in integers are there to the equation on the chalkboard?

Note: A solution here refers to an ordered triple (x,y,z).(x,y,z).

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