Jabarkan holds. dari Konjektur abc dalam bahasa melayu

A third formulation of the conjecture involves the quality

q(a, b, c) of the

triple (a, b, c), defined by:

q(4, 127, 131) = log(131) / log(rad(4·127·131)) = log(131) / log(2·127·131) = 0.46820…

q(3, 125, 128) = log(128) / log(rad(3·125·128)) = log(128) / log(30) = 1.426565…

A typical triple (a, b, c) of coprime positive integers with a + b = c will have c < rad(abc), i.e. q(a, b, c) < 1. Triples with q > 1 such as in the second example are rather special, they consist of numbers divisible by high powers of small prime numbers.

Konjektur abc menyatakan bahawa bagi setiap ε > 0, there exist only finitely many triples (a, b, c) of integer positif yang perdana secara relatif dengan a + b = c supaya q(a, b, c) > 1 + ε.

Whereas it is known that there are infinitely many triples (a, b, c) of coprime positive integers with a + b = c such that q(a, b, c) > 1, the conjecture predicts that only finitely many of those have q > 1.01 or q > 1.001 or even q > 1.0001, etc.