abc conjecture

Meanings

1. Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not).
2. Any of certain generalisations of the conjecture.

Etymology

From the names of the variables a, b, and c. The conjecture was proposed in 1985.