# Amphicheiral knot polynomials — H6

A knot \(K\subset S^3\) is called amphicheiral if an orientation-reversing homeomorphism of \(S^3\) maps \(K\) to itself; the homeomorphism may preserve or reverse the knot orientation.
For every amphicheiral knot \(K\), including the unknot, there exists \(f\in\mathbb Z[z]\) such that
\[
\nabla_K(z)\equiv f(z)f(-z)\pmod4.
\]
Here \(\nabla_K\) is the Conway polynomial normalized by \(\nabla_{\rm unknot}=1\), and the congruence is coefficientwise.