Fermat's last theorem over some small real quadratic fields

Using modularity, level lowering, and explicit computations with Hilbert modular forms, Galois representations, and ray class groups, we show that for 3 <= d <= 23, where d not equal 5, 17 and is squarefree, the Fermat equation x(n) + y(n) = z(n) has no nontrivial solutions over the quadratic field Q(root d) for n >= 4. Furthermore, we show that for d = 17, the same holds for prime exponents n equivalent to 3, 5 (mod 8).