Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture

Rafael von Känel, Benjamin Matschke

In the first part we construct algorithms which we apply to solve S-unit, Mordell, cubic Thue, cubic Thue-Mahler and generalized Ramanujan-Nagell equations. As a byproduct we obtai…