abcconjecture

ABC Conjecture

a+b=c, hcf(a, b)=1, c<=C_0rad(abc)

Disproof:

a=1

c<=C_0rad(abc) = C_0rad((c-1)c)

[let c->999999...]

->C_0rad(c^2) = C_0rad(c)

But c<=C_0rad(c) - clearly no bounds on C_0.