Quantum / CONCEPT

Divided differences over even and odd integer nodes are 2-adic units

Let z be distinct integer nodes indexed by a finite type, even on a set A of indices and odd off A, and let alpha = #A and beta = #A^c. If the binomial coefficient C(alpha + beta - 2, alpha - 1) is odd, then the partial divided-difference sum over the even nodes, the sum over i in A of 1 / prod_{j != i} (z i - z j), is a nonzero rational number of 2-adic valuation 0.