Submitted:
02 December 2025
Posted:
02 December 2025
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Abstract
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.
Keywords:
radical of an integer
; abc conjecture
; Diophantine equations
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