000  03796nam a22004815i 4500  

001  9780817646455  
003  DEHe213  
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007  cr nn 008mamaa  
008  100301s2009 xxu s  0eng d  
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_a9780817646455 _99780817646455 

024  7 
_a10.1007/b11856 _2doi 

050  4  _aQA241247.5  
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 : _bBirkhĂ¤user 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 problemsolving 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  _aZDB2SMA  
999 
_c369962 _d369962 