ABC conjecture and its implications - Koç, Tuğçe. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019)
In this thesis, our aim is to state the importance of abc conjecture and prove the strong results we obtain with the help of abc conjecture. First, we give necessary notions and tools which are used throughout the thesis. Then we introduce Hall conjecture, Fermat’s last theorem and Mordell conjecture, and their relations with abc conjecture. In particular, we give the eﬀective proof of Mordell conjecture using abc conjecture, given in the article of Noam Elkies, [1], and also get another height bound by combining with a diﬀerent theorem. Finally, we give three examples where we use both of the height bounds. This thesis was supported by T¨UB˙ITAK Project 117F274.
Keywords: Number theory.