The abc conjecture originated as the outcome of attempts by Oesterlé and Masser to understand the Szpiro conjecture about elliptic curves, [4] which involves more geometric structures in its statement …

If this conjecture were true, it would imply Fermat's last theorem for sufficiently large powers (Goldfeld 1996). This is related to the fact that the abc conjecture implies that there are at least non- Wieferich …

ABC Consequence Suppose the maximum quality of any abc-triple is known. Then we can find explicit bounds for the heights of points in CpK q.

May 20, 2025 · The celebrated abc conjecture asks whether every solution to the equation a + b = c in triples of coprime integers (a, b, c) must satisfy rad(abc)> Kεc1−ε, for some constant Kε> 0.

Nov 14, 2023 · ABC conjecture A conjectural relationship between the prime factors of two integers and those of their sum, proposed by David Masser and Joseph Oesterlé in 1985.

History of the conjecture This conjecture was formulated by mathematicians Joseph Oesterl ́e and David Masser in 1985 while studying the arithmetic of elliptic curves.

Jun 14, 2025 · The abc Conjecture was independently proposed by mathematicians David Masser and Joseph Oesterlé in the 1980s. It emerged from efforts to generalize certain properties of integers and …

The abc conjecture deals with pairs of numbers that have no common factors. Suppose a and b are two such numbers and that c is their sum. For example, if a = 3 and b = 7, then c = 3 + 7 = 10. Now, …

In 1991 Elkies [E] proved that the ABC–conjecture implies the Mordell conjecture (this was first proved by Faltings [F]) which states that every algebraic curve of genus 2 defined over Q has only finitely …

The ABC conjecture says that no matter how small Є, there will still be only finitely many examples where C counts as much bigger than rad (ABC). The problem is to prove or disprove the conjecture. …