abc Conjecture - Theoretical Results

Theoretical Results

The abc conjecture implies that c can be bounded above by a near-linear function of the radical of abc. However, exponential bounds are known. Specifically, the following bounds have been proven:

(Stewart & Tijdeman 1986),
(Stewart & Yu 1991), and
(Stewart & Yu 2001).

In these bounds, K1 is a constant that does not depend on a, b, or c, and K2 and K3 are constants that depend on ε (in an effectively computable way) but not on a, b, or c. The bounds apply to any triple for which c > 2.

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