Can You Solve the Equation X^2 + Y^2 + Z^2 = NXYZ for Natural N?

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SUMMARY

The equation X^2 + Y^2 + Z^2 = NXYZ, where N is a natural number, can be analyzed as a hyper-surface of dimension 2. In the context of Diophantine equations, specific integer solutions exist, such as (X, Y, Z, N) = (1, 1, 1, 3). Further clarification on the nature of the equation is essential for accurate problem-solving.

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hadi amiri 4
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can anyone give solution to this quation
x^2+y^2+z^2=nxyz n is natural
 
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(x, y, z, n) = (1, 1, 1, 3)
 


Hi,
The answer is described ad a hyper-surface of dimension 2 except if you are talking about a diophantic equation over the integers, please be more especific.
 

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