Polynomial parametrizations for two classes of Diophantine equations
We prove that the integer solution sets of two classes of Diophantine equations are finite unions of polynomial families with integer coefficients and unrestricted integer parameters. In the first class, each monomial, with at most one exception, contains a variable that occurs to the first power and in no other monomial. The second class consists of equations $M=f(t)$, where $M$ is a monomial independent of $t$ with a variable occurring to the first power, and $f\in\Z[t]$ splits completely over $\Q$. If $M$ involves at most two variables, $f$ may instead be an arbitrary quadratic…
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