Fermat's last theorem over some small real quadratic fields

Nuno Freitas, Samir Siksek
2015 Algebra & Number Theory  
Using modularity, level lowering, and explicit computations with Hilbert modular forms, Galois representations and ray class groups, we show that for 3 < d < 23 squarefree, d 5, 17, the Fermat equation x^n+y^n=z^n has no non-trivial solutions over the quadratic field Q(√(d)) for n > 4. Furthermore, we show for d=17 that the same holds for prime exponents n ≡ 3, 5 8.
doi:10.2140/ant.2015.9.875 fatcat:wadkf5ca2rdqfptlfyw4b3gzfu