On products of blocks of consecutive integers

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Date

2016

Author

Yıldız, Burak

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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.

Subject Keywords

Number theory., Polynomials., Algebraic number theory., Arithmetical algebraic geometry.

URI

http://etd.lib.metu.edu.tr/upload/12620171/index.pdf
https://hdl.handle.net/11511/25799

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

B. Yıldız, “On products of blocks of consecutive integers,” Ph.D. - Doctoral Program, Middle East Technical University, 2016.