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Sebastien Palcoux
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Does Mochizuki's proof of abc conjecture gives an upper-bound for the quality of a triple?

The quality of a triple $(a,b,c)$ of coprime positive integers such that $a + b = c$, is $$q=q(a,b,c) = \frac{log(c)}{log(rad(abc))}$$ Then $a+b = c = rad(abc)^{q(a,b,c)}$.
The triple with the highest known quality is $(2, 3^{10} \cdot 109, 23^5)$, with $q = 1.6299...$
If the abc conjecture is true then the quality of a triple should be bounded (expected by $2$).

Assuming Mochizuki's proof correct, does it gives an explicit upper-bound for the quality of a triple?

Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186