000			04669nam a22004693i 4500
001			EBC3074593
003			MiAaPQ
005			20240729124458.0
006			m o d |
007			cr cnu||||||||
008			240724s1998 xx o ||||0 eng d
020			_a9781447106135 _q(electronic bk.)
020			_z9783540761976
035			_a(MiAaPQ)EBC3074593
035			_a(Au-PeEL)EBL3074593
035			_a(CaPaEBR)ebr10917987
035			_a(OCoLC)958525644
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA241-247.5
082	0		_a512/.7
100	1		_aJones, Gareth A.
245	1	0	_aElementary Number Theory.
250			_a1st ed.
264		1	_aLondon : _bSpringer London, Limited, _c1998.
264		4	_c©1998.
300			_a1 online resource (305 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aSpringer Undergraduate Mathematics Series
505	0		_aCover -- Title -- Copyright -- Preface -- Contents -- Notes to the Reader -- 1. Divisibility -- 1.1 Divisors -- 1.2 Bezout's identity -- 1.3 Least common multiples -- 1.4 Linear Diophantine equations -- 1.5 Supplementary exercises -- 2. Prime Numbers -- 2.1 Prime numbers and prime-power factorisations -- 2.2 Distribution of primes -- 2.3 Fermat and Mersenne primes -- 2.4 Primality-testing and factorisation -- 2.5 Supplementary exercises -- 3. Congruences -- 3.1 Modular arithmetic -- 3.2 Linear congruences -- 3.3 Simultaneous linear congruences -- 3.4 Simultaneous non-linear congruences -- 3.5 An extension of the Chinese Remainder Theorem -- 3.6 Supplementary exercises -- 4. Congruences with a Prime-power Modulus -- 4.1 The arithmetic of Zp -- 4.2 Pseudoprimes and Carmichael numbers -- 4.3 Solving congruences mod (pe) -- 4.4 Supplementary exercises -- 5 Euler's Function -- 5.1 Units -- 5.2 Euler's function -- 5.3 Applications of Euler's function -- 5.4 Supplementary exercises -- 6. The Group of Units -- 6.1 The group Un -- 6.2 Primitive roots -- 6.3 The group Upe, where p is an odd prime -- 6.4 The group U2e -- 6.5 The existence of primitive roots -- 6.6 Applications of primitive roots -- 6.7 The algebraic structure of Un -- 6.8 The universal exponent -- 6.9 Supplementary exercises -- 7. Quadratic Residues -- 7.1 Quadratic congruences -- 7.2 The group of quadratic residues -- 7.3 The Legendre symbol -- 7.4 Quadratic reciprocity -- 7.5 Quadratic residues for prime-power moduli -- 7.6 Quadratic residues for arbitrary moduli -- 7.7 Supplementary exercises -- 8. Arithmetic Functions -- 8.1 Definition and examples -- 8.2 Perfect numbers -- 8.3 The Möbius Inversion Formula -- 8.4 An application of the Möbius Inversion Formula -- 8.5 Properties of the Möbius function -- 8.6 The Dirichlet product -- 8.7 Supplementary exercises.
505	8		_a9. The Riemann Zeta Function -- 9.1 Historical background -- 9.2 Convergence -- 9.3 Applications to prime numbers -- 9.4 Random integers -- 9.5 Evaluating '(2) -- 9.6 Evaluating (2k) -- 9.7 Dirichlet series -- 9.8 Euler products -- 9.9 Complex variables -- 9.10 Supplementary exercises -- 10 Sums of Squares -- 10.1 Sums of two squares -- 10.2 The Gaussian integers -- 10.3 Sums of three squares -- 10.4 Sums of four squares -- 10.5 Digression on quaternions -- 10.6 Minkowski's Theorem -- 10.7 Supplementary exercises -- 11. Fermat's Last Theorem -- 11.1 The problem -- 11.2 Pythagoras's Theorem -- 11.3 Pythagorean triples -- 11.4 Isosceles triangles and irrationality -- 11.5 The classification of Pythagorean triples -- 11.6 Fermat -- 11.7 The case n = 4 -- 11.8 Odd prime exponents -- 11.9 Lamé and Kummer -- 11.10 Modern developments -- 11.11 Further reading -- Appendix A. Induction and Well-ordering -- Appendix B. Groups, Rings and Fields -- Appendix C. Convergence -- Appendix D. Table of Primes p &lt -- 1000 -- Solutions to Exercises -- Bibliography -- Index of symbols -- Index of names -- Index.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aNumber theory.
655		4	_aElectronic books.
700	1		_aJones, Josephine M.
776	0	8	_iPrint version: _aJones, Gareth A. _tElementary Number Theory _dLondon : Springer London, Limited,c1998 _z9783540761976
797	2		_aProQuest (Firm)
830		0	_aSpringer Undergraduate Mathematics Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3074593 _zClick to View
999			_c67368 _d67368