Suppose we have two polynomials $f$, $g$ in $k[X_1, ..., X_n]$ over some field $k$, and they have no factor in common. Suppose that $f/g$ is symmetric. Must than $f$ and $g$ also both be symmetric?
Same question for homogeneous instead of symmetric.
2026-03-31 15:46:26.1774971986
If f/g is symmetric (resp homogeneous), must f and g be as well?
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