abc conjecture
The "abc conjecture" is a pivotal hypothesis in number theory, first proposed by Joseph Oesterlé and David Masser in 1985, exploring the relationship between the prime factors of three integers.
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Definition
C2Number Theory
(technical, academic)A hypothesis stating that for any three positive integers, a, b, and c, which are coprime and satisfy a + b = c, the product of their distinct prime factors is usually close in size to c.
Example
- The abc conjecture implies significant insights into other famous problems like Fermat's Last Theorem.
- Despite many efforts, the abc conjecture remains unproven and is a major open problem in number theory.