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Ahh you got me thinking here... Good thought on this. Please elaborate on the "prediction" part (yes you did state potentially)... I am curious and want to make sure I am following you..
The abc conjecture has a large number of consequences. These include both known results, and conjectures for which it gives a conditional proof.
Thue–Siegel–Roth theorem on diophantine approximation of algebraic numbers
Fermat's Last Theorem for all sufficiently large exponents (proven in general by Andrew Wiles)
The Mordell conjecture (Elkies 1991)
The Erdős–Woods conjecture except for a finite number of counterexamples (Langevin 1993)
The existence of infinitely many non-Wieferich primes (Silverman 1988)
The weak form of Marshall Hall's conjecture on the separation between squares and cubes of integers (Nitaj 1996)
The Fermat–Catalan conjecture, a generalization of Fermat's last theorem concerning powers that are sums of powers (Pomerance 2008)
The L function L(s,(−d/.)) formed with the Legendre symbol, has no Siegel zero (this consequence actually requires a uniform version of the abc conjecture in number fields, not only the abc conjecture as formulated above for rational integers)
P(x) has only finitely many perfect powers for integral x for P a polynomial with at least three simple zeros.
A generalization of Tijdeman's theorem
It is equivalent to the Granville–Langevin conjecture.
It is equivalent to the modified Szpiro conjecture, which would yield a bound of \operatorname[rad](abc)^[\frac+\epsilon] (Oesterlé 1988).
Dąbrowski (1996) has shown that the abc conjecture implies that n! + A= k2 has only finitely many solutions for any given integer A.[clarification needed]
While the first group of these have now been proven, the abc conjecture itself remains of interest, because of its numerous links with deep questions in number theory.