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On Some Properties of ABC Triples and Radicals of an Integer

by Cheng-Ting Wang

Posted: December 2, 2025
Server: Preprints.org
DOI: 10.20944/preprints202512.0286.v1

In this paper, we show that if a, b, c are numbers such that c = a + b, gcd(a, b, c) = 1 and rad(abc) < c, then c can’t be square free, at most one of a and b is square-free, and the square-free factor must be the smallest factor of the triple, we also showed an explicit upper bound for the quality of abc triples. We also discuss some basic properties of the radical function in general.

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