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#### Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces

(University of Waterloo, 2010-04-27)

We are interested in investigating the number of integral points on quadrics.
First, we consider non-degenerate plane conic curves defined over Z.
In particular we look at two types of conic sections: hyperbolas with ...

#### Infinite Sets of D-integral Points on Projective Algebrain Varieties

(University of Waterloo, 2005)

Let

**X**(**K**) ⊂ <strong>P</strong><sup>**n**</sup> (**K**) be a projective algebraic variety over**K**, and let**D**be a subset of <strong>P</strong><sup>**n**</sup><sub>**OK**</sub> such that the codimension of**D**with respect to**X**⊂ <strong>P</strong><sup>**n**</sup><sub>**OK**</sub> is two. We are interested in points**P**on**X**(**K**) with the property that the intersection of the closure of**P**and**D**is empty in <strong>P</strong><sup>**n**</sup><sub>**OK**</sub>, we call such points**D**-integral points on**X**(**K**). First we prove that certain algebraic varieties have infinitely many**D**-integral points. Then we find an explicit description of the complete set of all**D**-integral points in projective n-space over Q for several types of**D**....