Tuesday, August 28, 2012

Theorem - ABC Conjecture

Subject - Math
Period -
Creation - 1985
Founded by - J Oesterlé
Proponents - D W Masser

A conjecture stating that there exists a positive number k such that all positive integers a, b and c where:
a + b = c
(a, b, c) = 1
will result in:
z < G k
Where G is the greatest square-free factor of abc.

This has profound implications in the study of Diophantine equations which are indeterminate polynomial equations with integer inputs or variables. An example of such an implication is that the abc conjecture tells us the Fermat equation has at most a finite number of solutions.

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