turkmath.org

The asymptotic Fermat conjecture(AFC) states that for a number field K and for sufficiently large primes, the equation x^p+y^p+z^p=0 has only trivial solutions.  The strategy which is  referred as the "modular method" to solve the Fermat equation, used by Wiles in his famous proof, can be adapted to attack AFC and its several different generalizations.  Similar results are quite rare for other Fermat type equations such as x^p+y^q=z^r although the solutions of this equation have been studied over rationals.  In this talk, I will mention some recent asymptotic results  for the classical Fermat equation as well as some other Fermat type equations over number fields.

This talk is based on joint works with Isik and Ozman.