The ABC conjecture

http://news.yahoo.com/mathematician-claims-proof-connection-between-prime-numbers-131737044.html

base variables:
n = a number that can't be divided by the square of any number
sqp(n) = square-free part of number n
dpf(n) = distinct prime factor of n
>! = "always greater"

for pargraph 3:
dpf(n) * dpf(n) = sqp(n) || largest square-free number obtainable by this equation

for pragraph 4:

sqp(ABC)
-------   >!  0
   C

sqp(ABC)^1
-------   >!  1
   C