{"product_id":"9783319362557","title":"The Problem of Catalan","description":"\u003ch1\u003eThe Problem of Catalan\u003c\/h1\u003e \u003ch2\u003eBilu, Yuri F.; Bugeaud, Yann; Mignotte, Maurice\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn 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 other words, 3\u003csup\u003e2\u003c\/sup\u003e – 2\u003csup\u003e3\u003c\/sup\u003e = 1 is the only solution of the equation \u003ci\u003ex\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e – \u003ci\u003ey\u003csup\u003eq\u003c\/sup\u003e\u003c\/i\u003e = 1 in integers \u003ci\u003ex, y, p, q\u003c\/i\u003e with \u003ci\u003exy\u003c\/i\u003e ≠ 0 and \u003ci\u003ep, q \u003c\/i\u003e≥\u003ci\u003e \u003c\/i\u003e2.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn 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 a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2016-09-10\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319362557\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-10094-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 245\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":46547959939212,"sku":"9783319362557","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319362557.jpg?v=1772936897","url":"https:\/\/lateknightbooks.com\/products\/9783319362557","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}