Abc conjecture

The 'abc conjecture (also known as the Oesterlé–Masser conjecture') is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. It is stated in terms of three positive integers a, b and c (hence the name) that are relatively prime and satisfy a + b = c. The conjecture essentially states that the product of the distinct prime factors of abc is usually not much smaller than c. A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions. Mathematician Dorian Goldfeld described the abc conjecture as "The most important unsolved problem in Diophantine analysis".
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