Modular approcah to diophantine equations
| dc.contributor | Graduate Program in Mathematics. | |
| dc.contributor.advisor | Özman, Ekin. | |
| dc.contributor.author | Işık, Erman. | |
| dc.date.accessioned | 2023-03-16T11:21:46Z | |
| dc.date.available | 2023-03-16T11:21:46Z | |
| dc.date.issued | 2019. | |
| dc.description.abstract | In this thesis, we study the modular approach to the Fermat’s equation xp+yp = zp, where x,y and z are co-prime integers, and p is a prime, and some generalizations. After reviewing and explaining how the modular approach can be used to deal with the Fermat-type equations, following the paper of Emmanuel Halberstadt and Alain Karus, we prove that there exists a dense subset of the set of prime numbers such that the equation axp + byp = czp has no non-trivial primitive solution. Here a,b,c are fixed pairwise co-prime odd integers and p ≥ 5 is a prime. Then we show that the equation x4 + y2 = zp has no solutions in co-prime integers when p ≥ 211 due to Jordan Ellenberg’s article. The main idea to deal with this equation is based on the modularity of Q-curves and the images of Galois representations attached such curves. This thesis was supported by TUBITAK project 117F045. | |
| dc.format.extent | 30 cm. | |
| dc.format.pages | xi, 111 leaves ; | |
| dc.identifier.other | MATH 2019 I75 | |
| dc.identifier.uri | https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15309 | |
| dc.publisher | Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019. | |
| dc.subject.lcsh | Diophantine analysis. | |
| dc.subject.lcsh | Fermat numbers. | |
| dc.title | Modular approcah to diophantine equations |
Files
Original bundle
1 - 1 of 1