Constant C makes the ABC conjecture hold

The ABC conjecture in number theory was first proposed by Joseph Oesterlé and David Masser in 1985. Mathematicians declare this conjecture using three related positive integers a, b, and c (satisfying a+b=c). The conjecture states that if there are certain prime powers in the factors of a and b, then c is usually not divisible by the prime powers.

This paper utilizes the fact that the prime factor among all factors in the root number rad (c) can only be a power of 1. Then, analyze all combinations of c that satisfy rad (c)=c, calculate the value of the combination, and find the maximum and minimum values of the root number rad, as well as the maximum exponent between them. Using this maximum index, an equivalent inequality is constructed to prove the ABC conjecture.