The ABC Conjecture: A Profound Connection between Prime Factors and Integer Relationships

The ABC Conjecture is one of the most beautiful conjectures in number theory; it reveals a very strong link between the additive and multiplicative characteristics of integers. The conjecture holds (with few exceptions) that if three positive numbers a,b and c are a coprime and a+b=c, then the c is not significantly larger than the Multiplication of distinctive prime factors of abc (written rad (abc)). It presents an integrated review of the concept, some theoretical consequences, important examples of the concept; and potential uses in computational number theory, cryptography, and elsewhere.