abc conjecture

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|number theory}} Given [[coprime]] [[positive]] [[integer]]s ''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.

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