The Erdős-Selfridge and the Schinzel-Tijdeman theorems hold in $P{A}^{-}$

Abstract

We show that "The product of consecutive integers is never a power" and several results by Schinzel and Tijdeman on the solutions of the equation $y^m=P(x)$, for $m>1$, $y>1$, and $P(x)$ a polynomial with rational coefficients and with at least two distinct zeros, hold in a weak fragment of Peano Arithmetic, $P{A}^{-}$, which lacks any kind of induction, and whose models are the positive cones of discretely ordered rings.

arXiv commentThis paper has been withdrawn by the author. Paper withdrawn due to error in Proof of Lemma 3.2