Michael Stoll
Published 2010-02-23, updated 2010-03-16Version 2
These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one can solve a specific equation related to numbers occurring several times in Pascal's Triangle with state-of-the-art methods.
Comments: 10 pages, 2 figures. Added a missing known case and a reference (thanks to Benne de Weger).
On the Diophantine equation x^2+2^a.3^b.11^c=y^n
The Diophantine Equation $x^4 + 2 y^4 = z^4 + 4 w^4$---a number of improvements
On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(2x)^{k}=y^n$
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