{"product_id":"the-problem-of-catalan-von-yuri-f-bilu-yann-bugeaud-maurice-mignotte","title":"The Problem of Catalan","description":"\n                                \n                \u003cp\u003e\n                                        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 other words, 3\n                    \n                    \u003csup\u003e2\u003c\/sup\u003e\n                                         – 2\n                    \n                    \u003csup\u003e3\u003c\/sup\u003e\n                                         = 1 is the only solution of the equation \n                    \n                    \u003ci\u003e\n                                                x\n                        \n                        \u003csup\u003ep\u003c\/sup\u003e\n                                            \n                    \u003c\/i\u003e\n                                         – \n                    \n                    \u003ci\u003e\n                                                y\n                        \n                        \u003csup\u003eq\u003c\/sup\u003e\n                                            \n                    \u003c\/i\u003e\n                                         = 1 in integers \n                    \n                    \u003ci\u003ex, y, p, q\u003c\/i\u003e\n                                         with \n                    \n                    \u003ci\u003exy\u003c\/i\u003e\n                                         ≠ 0 and \n                    \n                    \u003ci\u003ep, q \u003c\/i\u003e\n                                        ≥\n                    \n                    \u003ci\u003e \u003c\/i\u003e\n                                        2.\n                \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e\u003c\/p\u003e\n                                \n                \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\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783319100937\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783319362557\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9783319100937","offer_id":40590567931997,"sku":"9783319100937","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9783319362557","offer_id":39426247426141,"sku":"9783319362557","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/d2d25b2c-a9cd-48e3-b1d3-24d1190bf672.jpg?v=1782536583","url":"https:\/\/shop.autorenwelt.de\/products\/the-problem-of-catalan-von-yuri-f-bilu-yann-bugeaud-maurice-mignotte","provider":"Autorenwelt Shop","version":"1.0","type":"link"}