LEADER 03432nam 22006255 450 001 9910299981103321 005 20200706113843.0 010 $a3-319-10094-7 024 7 $a10.1007/978-3-319-10094-4 035 $a(CKB)3710000000261935 035 $a(EBL)1965396 035 $a(OCoLC)893117743 035 $a(SSID)ssj0001372751 035 $a(PQKBManifestationID)11785454 035 $a(PQKBTitleCode)TC0001372751 035 $a(PQKBWorkID)11310892 035 $a(PQKB)10600316 035 $a(MiAaPQ)EBC1965396 035 $a(DE-He213)978-3-319-10094-4 035 $a(PPN)18209412X 035 $a(EXLCZ)993710000000261935 100 $a20141009d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Problem of Catalan /$fby Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (251 p.) 300 $aDescription based upon print version of record. 311 $a3-319-10093-9 320 $aIncludes bibliographical references and indexes. 327 $aAn Historical Account -- Even Exponents -- Cassels' Relations -- Cyclotomic Fields -- Dirichlet L-Series and Class Number Formulas -- Higher Divisibility Theorems -- Gauss Sums and Stickelberger's Theorem -- Mih?ilescu?s Ideal -- The Real Part of Mih?ilescu?s Ideal -- Cyclotomic units -- Selmer Group and Proof of Catalan's Conjecture -- The Theorem of Thaine -- Baker's Method and Tijdeman's Argument -- Appendix A: Number Fields -- Appendix B: Heights -- Appendix C: Commutative Rings, Modules, Semi-Simplicity -- Appendix D: Group Rings and Characters -- Appendix E: Reduction and Torsion of Finite G-Modules -- Appendix F: Radical Extensions. 330 $aIn 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 Mih?ilescu. In this book we give a complete and (almost) self-contained exposition of Mih?ilescu?s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory. 606 $aNumber theory 606 $aAlgebra 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aNumber theory. 615 0$aAlgebra. 615 14$aNumber Theory. 615 24$aGeneral Algebraic Systems. 615 24$aAlgebra. 676 $a511/.6 676 $a512.72 700 $aBilu$b Yuri F$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721239 702 $aBugeaud$b Yann$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMignotte$b Maurice$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299981103321 996 $aThe Problem of Catalan$92540401 997 $aUNINA LEADER 01151nam0 22002771i 450 001 UON00460864 005 20231205105123.787 100 $a20151113d1963 |0itac50 ba 101 $arus 102 $aRU 105 $a|||| 1|||| 200 1 $aZapiski pisma$fI. I. Gorba?evskij$gIzdanie podgotovili B. E. Syroe?kovskij, L. A. Sokol'skij, I. V. Poroch. Moskva$eIzd. Akademii nauk SSSR, 1963 210 $a352 p.$ctav. ; 22 cm. 620 $aRU$dMoskva$3UONL003152 676 $a891.709$cLetteratura russa. Storia, geografia, persone$v21 700 1$aGORBA?EVSKIJ$bIvan Ivanovi?$3UONV229198$0719572 702 1$aPOROCH$bIgor' Vasil'evi?$3UONV229071 702 1$aSOKOL'SKIJ$bL. A.$3UONV229130 702 1$aSYROE?KOVSKIJ$bB. E.$3UONV229129 712 $aAkademija Nauk SSSR$3UONV247334$4650 801 $aIT$bSOL$c20241213$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00460864 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI RUSSO C 1874 $eSI SLA1964 7 1874 996 $aZapiski pisma$91397302 997 $aUNIOR