Suppose that \( x, y, z \) are positive integers satisfying
\[
0 \leq x^2 + y^2 – xyz \leq z+1.
\]
Prove that \( x^2 + y^2 – xyz \) is a perfect square.
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2020-07 Perfect square,
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Suppose that \( x, y, z \) are positive integers satisfying
\[
0 \leq x^2 + y^2 – xyz \leq z+1.
\]
Prove that \( x^2 + y^2 – xyz \) is a perfect square.