Do these weird morphisms exist?
A "morphism" $\phi$ from $Z$ into some other set that doesn't make this
trivial, $S$ such that $\phi(a)^3 + \phi(b)^3 - \phi(c)^5 = \phi(a^3 + b^3
- c^5), \forall a,b,c \in Z$, and $0 \mapsto 0$? And the structure $S$ is
a ring? The formula immediately shows $\phi(-1) = -\phi(1)$, $\phi(1)^3 =
\phi(1)$, etc. It would be nice.
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