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Diophantine Equationsmedium
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How many integer solutions (x,y,z)(x, y, z)(x,y,z) with x,y,z≥0x, y, z \geq 0x,y,z≥0 satisfy x2+y2+z2≤6x^2 + y^2 + z^2 \leq 6x2+y2+z2≤6?