Mochizuki's abc conjecture

Mochizuki's abc conjecture investigates the relationships between three positive integers \(a\), \(b\), and \(c\) that satisfy \(a + b = c\). It suggests that, usually, when \(a\), \(b\), and \(c\) have no common prime factors, the size of \(c\) is rarely much larger than the product of the distinct prime factors involved in \(a\) and \(b\). In essence, it proposes a bound limiting how "unexpectedly" large the sum \(c\) can be relative to the prime factors of \(a\) and \(b\). This conjecture has deep implications for understanding the distribution of prime numbers and properties of integers.