On products of blocks of consecutive integers

---

Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2016

Öğrenci: BURAK YILDIZ

Danışman: MUSTAFA HURŞİT ÖNSİPER

Özet:

In this thesis, an old conjecture of Erdös and Graham concerning integer squares obtained from products of disjoint blocks of consecutive integers is revisited. From arithmetic geometry point of view, the conjecture concerns the structure of integral points on certain projective hypersurfaces. These hypersurfaces are analyzed geometrically. The relation between the Erdös-Graham conjecture and some well-known conjectures in diophantine geometry and in number theory are explained. As for the computational aspect of the problem, an efficient algorithm for computer search is developed and in certain computationally challenging cases new numerical examples are obtained.