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In 1842 the Belgian mathematician Eugene 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 other words, 3² - 2³ = 1 is the only solution of the equation x^p - y^q = 1 in integers x, y, p, q with xy 0 and p, q >= 2.

In this book we give a complete and (almost) self-contained exposition of Mihăilescu's work, which must...

In 1842 the Belgian mathematician Eugene 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 other words, 3² - 2³ = 1 is the only solution of the equation x^p - y^q = 1 in integers x, y, p, q with xy 0 and p, q >= 2.

In this book we give a complete and (almost) self-contained exposition of Mihăilescu's work, which must...