LEADER 06083nam 22005295 450 001 9910479869403321 005 20200702062217.0 010 $a1-4471-0613-X 024 7 $a10.1007/978-1-4471-0613-5 035 $a(CKB)3400000000088227 035 $a(SSID)ssj0000806031 035 $a(PQKBManifestationID)11422703 035 $a(PQKBTitleCode)TC0000806031 035 $a(PQKBWorkID)10746923 035 $a(PQKB)11536793 035 $a(DE-He213)978-1-4471-0613-5 035 $a(MiAaPQ)EBC3074593 035 $a(PPN)237990687 035 $a(EXLCZ)993400000000088227 100 $a20121227d1998 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aElementary Number Theory$b[electronic resource] /$fby Gareth A. Jones, Josephine M. Jones 205 $a1st ed. 1998. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d1998. 215 $a1 online resource (XIV, 302 p.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-76197-7 320 $aIncludes bibliographical references and indexes. 327 $a1. 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 ?p -- 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 Une, 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 Mobius Inversion Formula -- 8.4 An application of the Mobius Inversion Formula -- 8.5 Properties of the Mobius function -- 8.6 The Dirichlet product -- 8.7 Supplementary exercises -- 9. 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 Lame and Kummer -- 11.10 Modern developments -- 11.11 Further reading -- Solutions to Exercises -- Index of symbols -- Index of names. 330 $aOur intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back­ ground or maturity from the reader, and which can be read and understood with no extra assistance. Our first three chapters are based almost entirely on A-level mathematics, while the next five require little else beyond some el­ ementary group theory. It is only in the last three chapters, where we treat more advanced topics, including recent developments, that we require greater mathematical background; here we use some basic ideas which students would expect to meet in the first year or so of a typical undergraduate course in math­ ematics. Throughout the book, we have attempted to explain our arguments as fully and as clearly as possible, with plenty of worked examples and with outline solutions for all the exercises. There are several good reasons for choosing number theory as a subject. It has a long and interesting history, ranging from the earliest recorded times to the present day (see Chapter 11, for instance, on Fermat's Last Theorem), and its problems have attracted many of the greatest mathematicians; consequently the study of number theory is an excellent introduction to the development and achievements of mathematics (and, indeed, some of its failures). In particular, the explicit nature of many of its problems, concerning basic properties of inte­ gers, makes number theory a particularly suitable subject in which to present modern mathematics in elementary terms. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aNumber theory 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a512/.7 700 $aJones$b Gareth A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0116364 702 $aJones$b Josephine M$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910479869403321 996 $aElementary Number Theory$92245176 997 $aUNINA LEADER 03548nam 2200685 450 001 9910462455903321 005 20200520144314.0 010 $a1-4426-9008-9 024 7 $a10.3138/9781442690080 035 $a(CKB)2670000000186109 035 $a(OCoLC)785802925 035 $a(CaPaEBR)ebrary10541178 035 $a(SSID)ssj0000622904 035 $a(PQKBManifestationID)11451289 035 $a(PQKBTitleCode)TC0000622904 035 $a(PQKBWorkID)10647932 035 $a(PQKB)10856816 035 $a(CEL)439890 035 $a(CaBNVSL)slc00228446 035 $a(MiAaPQ)EBC3279040 035 $a(MiAaPQ)EBC4672737 035 $a(DE-B1597)479135 035 $a(OCoLC)987934746 035 $a(DE-B1597)9781442690080 035 $a(Au-PeEL)EBL4672737 035 $a(CaPaEBR)ebr11258391 035 $a(OCoLC)958559311 035 $a(EXLCZ)992670000000186109 100 $a20160914h20112011 uy 0 101 0 $aeng 135 $aurcn||||||a|| 181 $ctxt 182 $cc 183 $acr 200 10$aGambling for profit $elotteries, gaming machines, and casinos in cross-national focus /$fKerry G.E. Chambers 210 1$aToronto, [Ontario] ;$aBuffalo, [New York] ;$aLondon, [England] :$cUniversity of Toronto Press,$d2011. 210 4$dİ2011 215 $a1 online resource (296 p.) 311 $a1-4426-4189-4 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tFigures and Tables -- $tPreface -- $tAbbreviations -- $t1. The Emergence of Gambling within a Historically Contingent Framework -- $t2. Gambling for Profit in the Welfare Regimes -- $t3. Casinos in Australia, Canada, and the United States -- $t4. Lotteries and Gaming Machines in Australia, Canada, and the United States -- $t5. Historical Contingency in Political-Economic and Sociocultural Contexts -- $tNotes -- $tGlossary -- $tReferences -- $tIndex 330 $aOver the past forty years, Western governments have increasingly liberalized and deregulated gambling, which is now used to deliver state revenues and commercial profit in many jurisdictions. Gambling for Profit is a cross-national history of the emergence of legal gambling, including lotteries, gaming machines, and casinos.Gambling for Profit is unique among studies of gambling's twentieth-century growth thanks to Kerry G.E. Chambers's strong analytical framework - investigating not only the political aspects of legalization, but also the sociocultural factors that influence popular adoption. Chambers provides a useful chronological examination of the electronic gambling phenomenon, as well as comparative data on dates of introduction and revenues across twenty-three countries. Gambling for Profit provides a dynamic model to explore the legalization of gambling and stresses the inadequacy of seeking universal explanations for gambling's entrenchment within particular cultures. 606 $aGambling$vCross-cultural studies 606 $aGambling$xSocial aspects 606 $aGambling$xGovernment policy 606 $aGambling$xEconomic aspects 608 $aElectronic books. 615 0$aGambling 615 0$aGambling$xSocial aspects. 615 0$aGambling$xGovernment policy. 615 0$aGambling$xEconomic aspects. 676 $a306.4/82 700 $aChambers$b Kerry$f1958-$0973897 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462455903321 996 $aGambling for profit$92216480 997 $aUNINA LEADER 01013nam0 22002531i 450 001 UON00216580 005 20231205103356.497 010 $a58-685-9043-0 100 $a20030730d1997 |0itac50 ba 101 $arus 102 $aRU 105 $a|||| ||||| 200 1 $aImperator Nikolaj Pervyj$eego ?izn' i carstvovanie$fN. 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