Insulators of ABC Solutions

James E. Weigandt

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arXiv · 1401.6439

Insulators of ABC Solutions

James E. Weigandt

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Abstract

This note studies various ways of measuring the complexity of primitive solutions to the equation $A \,+\, B\, + \,C = 0$ and conjectures relating them. We define the insulator $\mathcal I(A,B,C)$ of a primitive solution as the smallest positive integer $\mathcal I$ such that the primes dividing the product $ABC \cdot \mathcal I$ are exactly those below a given bound. We show that the strong XYZ Conjecture of Lagarias and Soundararajan implies there are only finitely many primitive solutions $(A,B,C)$ with a given insulator.

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James E. Weigandt. 2014-01-24. Insulators of ABC Solutions. https://arxiv.org/abs/1401.6439

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