# Amphicheiral knot polynomials — H5

Let \(K\subset S^3\) be an oriented knot admitting a finite-order orientation-reversing diffeomorphism of \(S^3\) that preserves the orientation of \(K\). Let \(\nabla_K(z)\in\mathbb Z[z]\) be its Conway polynomial, normalized by \(\nabla_{\rm unknot}=1\).
There exists \(f\in\mathbb Z[z]\) such that
\[
\nabla_K(z)\equiv f(z)f(-z)\pmod4,
\]
where the congruence is coefficientwise.