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001			290914
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008			150903s2008 xxk| o |||| 0|eng d
020			_a9781848001855 _99781848001855
024	7		_a10.1007/9781848001855 _2doi
035			_avtls000344203
039		9	_a201509030354 _bVLOAD _c201405050304 _dVLOAD _y201402061250 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA241-247.5
100	1		_aSchoof, René. _eautor _9305807
245	1	0	_aCatalan's Conjecture / _cby René Schoof.
250			_a1.
264		1	_aLondon : _bSpringer London : _bImprint: Springer, _c2008.
300			_aIx, 124 páginas 10 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aUniversitext, _x0172-5939
500			_aSpringer eBooks
505	0		_aThe Case “q = 2” -- The Case “p = 2” -- The Nontrivial Solution -- Runge’s Method -- Cassels’ theorem -- An Obstruction Group -- Small p or q -- The Stickelberger Ideal -- The Double Wieferich Criterion -- The Minus Argument -- The Plus Argument I -- Semisimple Group Rings -- The Plus Argument II -- The Density Theorem -- Thaine’s Theorem.
520			_aEugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it. Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The first few sections of the book require little more than a basic mathematical background and some knowledge of elementary number theory, while later sections involve Galois theory, algebraic number theory and a small amount of commutative algebra. The prerequisites, such as the basic facts from the arithmetic of cyclotomic fields, are all discussed within the text. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further. Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9781848001848
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-1-84800-185-5 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c290914 _d290914