The Diophantine Equation
Frederic C Barnett · UNM’s Digital Repository (University of New Mexico) · 1951
In the first part of Chapter II of this thesis a study is made of these surfaces Fn. In the second part of Chapter II, several differential geometric properties of Fn are adduced, and again, an attack based on certain of these is shown to lead to the very theorem we seek to prove. Finally, we obtain three geometrical implications of the assumption that an integral triad exists on Fn suggesting new lines of attack on the theorem of Fermat.