Special case of Fermat's Theorem

Abstract

We prove under a mild condition that the only rationals x, y with x ≥ 0, y≥ 0 and x+y=N(k), for some k ∈ Q*, and x^p+y^p=1 are x=0, y=1 and x=1, y=0. Here, we let N denote the norm from Q(ω_p) to Q for p an odd prime number.