LEADER 04452oam 2200601 450 001 9910153066003321 005 20230803220501.0 010 $a1-292-05541-3 035 $a(CKB)2550000001160263 035 $a(SSID)ssj0001256955 035 $a(PQKBManifestationID)12453002 035 $a(PQKBTitleCode)TC0001256955 035 $a(PQKBWorkID)11272667 035 $a(PQKB)11366660 035 $a(MiAaPQ)EBC5186064 035 $a(MiAaPQ)EBC5176520 035 $a(MiAaPQ)EBC5831743 035 $a(MiAaPQ)EBC5138770 035 $a(MiAaPQ)EBC6399970 035 $a(Au-PeEL)EBL5138770 035 $a(CaONFJC)MIL543468 035 $a(OCoLC)1002640302 035 $a(EXLCZ)992550000001160263 100 $a20210428d2014 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA friendly introduction to number theory /$fJoseph H. Silverman 205 $aFourth, Pearson new international edition. 210 1$aHarlow, England :$cPearson,$d[2014] 210 4$d©2014 215 $a1 online resource (459 pages) $cillustrations 225 1 $aPearson custom library 300 $aIncludes index. 311 $a1-292-02709-6 311 $a1-306-12217-1 327 $aCover -- Table of Contents -- 1. What is Number Theory? -- 2. Pythagorean Triples -- 3. Pythagorean Triples and the Unit Circle -- 4. Sums of Higher Powers and Fermat's Last Theorem -- 5. Divisibility and the Greatest Common Divisor -- 6. Linear Equations and the Greatest Common Divisor -- 7. Factorization and the Fundamental Theorem of Arithmetic -- 8. Congruences -- 9. Congruences, Powers, and Fermat's Little Theorem -- 10. Congruences, Powers, and Euler's Formula -- 11. Euler's Phi Function and the Chinese Remainder Theorem -- 12. Prime Numbers -- 13. Counting Primes -- 14. Mersenne Primes -- 15. Mersenne Primes and Perfect Numbers -- 16. Powers Modulo m and Successive Squaring -- 17. Computing kth Roots and Modulo m -- 18. Powers, Roots, and "Unbreakable" Codes -- 19. Primality Testing and Carmichael Numbers -- 20. Squares Modulo p -- 21. Quadratic Reciprocity -- 22. Proof of Quadratic Reciprocity -- 23. Which Primes Are Sums of Two Squares? -- 24. Which Numbers are Sums of Two Squares? -- 25. Euler's Phi Function and Sums of Divisors -- 26. Powers Modulo p and Primitive Roots -- 27. Primitive Roots and Indices -- 28. The Equation X4+Y4=Z4 -- 29. Square-Triangular Numbers Revisited -- 30. Pell's Equation -- 31. Diophantine Approximation -- 32. Diophantine Approximation and Pell's Equation -- 33. Number Theory and Imaginary Numbers -- 34. The Gaussian Integers and Unique Factorization -- 35. Irrational Numbers and Transcendental Numbers -- 36. Binomial Coefficients and Pascal's Triangle -- 37. Fibonacci's Rabbits and Linear Recurrence Sequences -- 38. Cubic Curves and Elliptic Curves -- 39. Elliptic Curves with Few Rational Points -- 40. Points on Elliptic Curves Modulo p -- 41. Torsion Collections Modulo p and Bad Primes -- 42. Defect Bounds and Modularity Patterns -- 43. Elliptic Curves and Fermat's Last Theorem. 327 $a44. The Topsy-Turvy World of Continued Fractions -- 45. Continued Fractions and Pell's Equation -- 46. Generating Functions -- 47. Sums of Powers -- 48. Appendix: A List of Primes -- Index. 330 $aFor one-semester undergraduate courses in Elementary Number Theory.   A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results. 410 0$aPearson custom library. 606 $aNumber theory$vTextbooks 615 0$aNumber theory 676 $a512.7 700 $aSilverman$b Joseph H.$f1955-$057147 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a9910153066003321 996 $aA friendly introduction to number theory$93411148 997 $aUNINA