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arXiv · 1410.8441

The Erd\H{o}s-Selfridge and the Schinzel-Tijdeman theorems hold in $PA^-$

Victor Pambuccian
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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, $PA^-$, which lacks any kind of induction, and whose models are the positive cones of discretely ordered rings.

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Victor Pambuccian. 2014-10-30. The Erd\H{o}s-Selfridge and the Schinzel-Tijdeman theorems hold in $PA^-$. https://arxiv.org/abs/1410.8441

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