Strongly Commuting Ring and The Prounet-Tarry-Escott Problem

In 1935, Wright conjectured that ideal solutions to the PTE problem in Diophantine number theory should exist. In this paper, we prove Wright’s conjecture holds true based on the the representation theory of the minuscule strongly commuting ring introduced by Kostant in 1975 and the complex coefficient cohomology ring structures of the Grassmannian variey.