Theorem: h\colon\pi_{2n-1}(S^n)\to\mathbb{Z} is a homomorphism.
The Hopf invariant is 1 for the Hopf maps (where n=1,2,4,8, corresponding to the real division algebras \mathbb{A}=\mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O}, respectively, and to the fibration S(\mathbb{A}^2)\to\mathbb{PA}^1 sending a direction on the sphere to the subspace it spans).