abc conjecture

The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory, first proposed by JosephOesterlé (1985) and DavidMasser (1988). 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. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d is usually not much smaller than c. In other words: if a and b are composed from large powers of primes, then c is usually not divisible by large powers of primes. The precise statement is given below.