Based on Katz’s equidistribution framework, we give a one-dimensional proof of a function-field analogue of a conjecture of Erdős in the large-q regime: for squarefree f of degree n, every class in \((\mathbb {F}_q[t]/(f))^\times \) is represented as a product of two monic irreducibles of degrees \(\le n\) once q is sufficiently large in terms of n. The proof yields a uniform \(q^{-1/2}\) -saving in the relevant twisted character sums, with an explicit constant depending on n. Sawin [12] proved a stronger and more general result by higher-dimensional sheaf-theoretic methods; the present note instead emphasizes a simpler one-dimensional argument within Katz’s framework.
