The generalized Fermat finiteness conjecture over the integers

Let $A,B,C\in\mathbb{Z}$ satisfy $\gcd(A,B,C)=1$. For prime exponents $p,q,r$ with

$$\frac{1}{p}+\frac{1}{q}+\frac{1}{r}<1,$$

a non-trivial primitive integer solution of $Ax^p+By^q+Cz^r=0$ is a solution with $xyz\ne0$ and $\gcd(x,y,z)=1$. Generalized Fermat finiteness conjecture. Over all choices of such prime exponents $p,q,r$, the generalized Fermat equation $Ax^p+By^q+Cz^r=0$ has only finitely many non-trivial primitive integer solutions. This is a finiteness conjecture for generalized Fermat equations; the supplied text gives no resolution status.