Mathematics – Algebraic Geometry
Scientific paper
2008-01-09
Mathematics
Algebraic Geometry
12 pages
Scientific paper
Let P(x,y) be a rational polynomial and k in Q be a generic value. If the curve (P(x,y)=k) is irreducible and admits an infinite number of points whose coordinates are integers then there exist algebraic automorphisms that send P(x,y) to the polynomial x or to x^2-dy^2. Moreover for such curves (and others) we give a sharp bound for the number of integral points (x,y) with x and y bounded.
Bodin Arnaud
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