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.
Read more about this topic: abc Conjecture
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