## product description page

# Problem of Catalan (Reprint) (Paperback) (Yuri Bilu)

### about this item

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 Mihailescu. In other words, 3^{2}– 2^{3} = 1 is the only solution of the equation *x ^{p}*–

*y*= 1 in integers

^{q}*x, y, p, q*with

*xy*? 0 and

*p, q*=2.

In this book we give a complete and (almost) self-contained exposition of Mihailescu’s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.

**Edition:**Reprint

**Genre:**Mathematics

**Format:**Paperback

**Publisher:**Springer Verlag

**Author:**Yuri Bilu

**Language:**English

**Street Date**: September 30, 2016

**TCIN**: 51746279

**UPC**: 9783319362557

**Item Number (DPCI)**: 248-31-0850

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