Generalised Fermat equation: a survey of solved cases

Ashleigh Ratcliffe, Bogdan Grechuk

Generalised Fermat equation (GFE) is the equation of the form $a{x}^p+b{y}^q=c{z}^r$, where $a,b,c,p,q,r$ are positive integers. If $1/p+1/q+1/r<1$, GFE is known to have at most finitely…