The Diophantine Equation: αν = βν + γν

This text represents my work on the solutions of the Diophantine Equation:αν = βν + γν, for ν = 2, 4, 3, 5, 7, 11… (odd prime).Recognizing that this difficult work has many errors, I will appreciate it very much, if in time, you send to me via the publisher, your comments and corrections, so that the next edition be better.The proof of the non-existence of solutions of the above equation, for: ν = 3, 4, 5, 7, 11…, will be and proof of the relative FERMAT’S proposal with title:“FERMAT’S LAST THEOREM” (F.L.T.).