The surfaces V(x1^{a1} + x2^{a2} + x3^{a3} + 1 = 0) in affine 3-space are isomorphic if and only if the exponent triples (a1,a2,a3) are permutations of each other, for all ai >= 2.
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The Isomorphism Classes of the Surfaces $x_1^{a_1} + x_2^{a_2} + x_3^{a_3} + 1 = 0$
The surfaces V(x1^{a1} + x2^{a2} + x3^{a3} + 1 = 0) in affine 3-space are isomorphic if and only if the exponent triples (a1,a2,a3) are permutations of each other, for all ai >= 2.