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Published in:
2010 | OriginalPaper | Chapter
Pell-Type Equations
Authors : Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Published in: An Introduction to Diophantine Equations
Publisher: Birkhäuser Boston
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In 1909, A. Thue proved the following important theorem:
Let f
=
a
n
z
n
+
a
n
-1
z
n
-1
+…+
a
1
z
+
a
0
be an irreducible polynomial of degree
≥ 3
with integral coefficients. Consider the corresponding homogeneous polynomial
$$F(x,y)=y^nf\left(\frac{x}{y}\right)=a_nx^n+a_{n-1}x^{n-1}y+\cdots+a_1xy^{n-1}+a_0y^n.$$