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Explore the first lecture of MINICOURSE 4 on Diophantine equations with few solutions, presented by Hector Pasten from PUC, Chile, as part of the AGRA IV (Arithmetic, Groups and Analysis) series. Delve into the intricacies of this mathematical topic over the course of 50 minutes, gaining insights from an expert in the field. This lecture, conducted in Spanish, offers a comprehensive introduction to the subject, setting the foundation for further exploration in subsequent sessions of the minicourse.