{"product_id":"the-problem-of-catalan-yuri-f-bilu-9783319362557","title":"The Problem of Catalan","description":"\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\u0026gt;=\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Yuri F. Bilu,Yann Bugeaud,Maurice Mignotte\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3319362550\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783319362557\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/10\/2016\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 245\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.81lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.55d","brand":"Yuri F. Bilu","offers":[{"title":"Paperback","offer_id":48996284793087,"sku":"9783319362557","price":54.99,"currency_code":"USD","in_stock":true}],"url":"https:\/\/www.whiterainbookhouse.com\/products\/the-problem-of-catalan-yuri-f-bilu-9783319362557","provider":"WR Book House","version":"1.0","type":"link"}