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In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In this book we give a complete and (almost) self-contained exposition of Mihăilescu’s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.

Catalan language --- Social aspects. --- Romance languages --- Number theory. --- Algebra. --- Number Theory. --- General Algebraic Systems. --- Mathematics --- Mathematical analysis --- Number study --- Numbers, Theory of --- Algebra

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