In number theory, when you try to solve an equation in a number field, it is often more convenient to work with ideals than with integers. This stems from the fact that ideals have unique factorization, but integers may not. I will explain the advantages and difficulties of this method using concrete examples. The seminar takes place in PORTO. (*) Peter Lombaers is a PhD student of the Joint PhD Program UCUP, working at the University of Porto, in Number Theory, under the supervision of Professor António José Machiavelo.
