000 03796nam a22004815i 4500
001 978-0-8176-4645-5
003 DE-He213
005 20180115171437.0
007 cr nn 008mamaa
008 100301s2009 xxu| s |||| 0|eng d
020 _a9780817646455
_9978-0-8176-4645-5
024 7 _a10.1007/b11856
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aAndrica, Dorin.
_eauthor.
245 1 0 _aNumber Theory
_h[electronic resource] :
_bStructures, Examples, and Problems /
_cby Dorin Andrica, Titu Andreescu.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2009.
300 _aXVIII, 384 p. 2 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aFundamentals -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous Problems -- Solutions to Additional Problems -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous Problems.
520 _aNumber theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This lively introductory text focuses on a problem-solving approach to the subject. Key features of Number Theory: Structures, Examples, and Problems: * A rigorous exposition starts with the natural numbers and the basics. * Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties. * Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered. * Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems. * Glossary, bibliography, and comprehensive index round out the text. Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aNumber theory.
650 0 _aCombinatorics.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aMathematics, general.
650 2 4 _aAlgebra.
650 2 4 _aCombinatorics.
700 1 _aAndreescu, Titu.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817632458
856 4 0 _uhttp://dx.doi.org/10.1007/b11856
912 _aZDB-2-SMA
999 _c369962
_d369962