An algebraic proof of Colombo's difference-power determinant conjecture

Let $n\ge2$ be even, let $λ=(λ_1,\ldots,λ_n)\in\mathbb{R}^n$ have pairwise distinct coordinates, and define the difference-power matrix \[ A_d(λ) := \bigl[(λ_r-λ_s)^d\bigr]_{r,s=1}^n, \qquad d\in\mathbb{N}. \] In 1928, Colombo proved that $\det A_{n-1}(λ)\ne0$---and hence $\det A_{n-1}(λ)>0$---and t