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A friendly introduction to number theory / Joseph H. Silverman

By: Silverman, Joseph H, 1955-.
Publisher: Upper Saddle River, N.J. : Prentice Hall, c2001Edition: 2nd ed.Description: vii, 386 p. ; 24 cm.ISBN: 0130309540.Subject(s): Number theoryDDC classification: 512.7
Contents:
Ch.30. Diophantine approximation. - Ch.31. Diophantine approximation and Pell's equation. - Ch.32. Primality testing and carmichael number. - Ch.33. Number theory and imaginary number. - Ch.34. The Gaussian integers and unique factorization. - Ch.35. Irrational number and transcendental numbers. - Ch.36. Binomial coeffecients and Pascal's triangle. - Ch.37. Fibonacci's rabbits and linear recurrence sequences. - Ch.38. Generating functions. - Ch.39. Sums of powers. - Ch.40. Cubic curves and Ellipric curves. - Ch.41. Elliptic curves with few rational points. - Ch.42. Points on Elliptic curves modulo p. - Ch.43. Torsion collections modulo p and bad primes. - Ch.44. Defect bounds and modularity pattens. - Ch.45. Elliptic curves and Fermat's last theorem further reading. - Appendix A. Factorization of small composite integers. - Appendix B. A list of primes - Index
Preface. - Introduction. - Ch.1. What is number theory?. - Ch.2. Pythagorean triples. - Ch.3. Pythagorean triples and the unit circle. - Ch.4. Sums of higher powers and Fermat's last theorem. - Ch.5. Divisibility and the greatest common divisor. - Ch.6. Linear equations and the greatest common divisor. - Ch.7. Factorization and the fundamental theorem of arithmetic. - Ch.8. Congruences. - Ch.9. Congruences, power and Fermat's little theorem. - Ch.10. Congruences, power, and Euler's formula. - Ch.11. Euler's Phi function. - Ch.12. Prime numbers. - Ch.13. Counting primes. - Ch.14. Mersenne primes. - Ch.15. Mersenne primes and perfect numbers. - Ch.16. Powers modulo m and successive squaring. - Ch.17. Computing kth roots modulo m. - Ch.18. Powers, roots and "Unbreakable" codes. - Ch.19. Euler's Phi function and sums of divisors. - Ch.20. Powers modulo p and primitive roots. - Ch.21. Primitive roots and indices. - Ch.22. Squares modulo p. - Ch.23. Is-1a square Modulo p?Is 2?. - Ch.24. Quadratic reciprocity. - Ch.25. Which primes are sums of two squares? - Ch.26. Which numbers are sums of two squares?. - Ch.27. The equation X4+Y4+Z4. - Ch.28. Square-triangular number revisited. - Ch.29. Pell's equation.
Summary: ...This book will lead you through the groves wherein lurk some of the brightest flowers of number theory, as it simultaneously encourages you to investigate, analyze, conjecture, and ultimate prove your own beautiful number theoritics results. - Preface
Item type Current location Call number Copy number Status Notes Date due Barcode
Main Collection Taylor's Library-TU
512.7 SIL (Browse shelf) 1 Available SOCIT,15004,03,CL 1000109960

Ch.30. Diophantine approximation. - Ch.31. Diophantine approximation and Pell's equation. - Ch.32. Primality testing and carmichael number. - Ch.33. Number theory and imaginary number. - Ch.34. The Gaussian integers and unique factorization. - Ch.35. Irrational number and transcendental numbers. - Ch.36. Binomial coeffecients and Pascal's triangle. - Ch.37. Fibonacci's rabbits and linear recurrence sequences. - Ch.38. Generating functions. - Ch.39. Sums of powers. - Ch.40. Cubic curves and Ellipric curves. - Ch.41. Elliptic curves with few rational points. - Ch.42. Points on Elliptic curves modulo p. - Ch.43. Torsion collections modulo p and bad primes. - Ch.44. Defect bounds and modularity pattens. - Ch.45. Elliptic curves and Fermat's last theorem further reading. - Appendix A. Factorization of small composite integers. - Appendix B. A list of primes - Index

Preface. - Introduction. - Ch.1. What is number theory?. - Ch.2. Pythagorean triples. - Ch.3. Pythagorean triples and the unit circle. - Ch.4. Sums of higher powers and Fermat's last theorem. - Ch.5. Divisibility and the greatest common divisor. - Ch.6. Linear equations and the greatest common divisor. - Ch.7. Factorization and the fundamental theorem of arithmetic. - Ch.8. Congruences. - Ch.9. Congruences, power and Fermat's little theorem. - Ch.10. Congruences, power, and Euler's formula. - Ch.11. Euler's Phi function. - Ch.12. Prime numbers. - Ch.13. Counting primes. - Ch.14. Mersenne primes. - Ch.15. Mersenne primes and perfect numbers. - Ch.16. Powers modulo m and successive squaring. - Ch.17. Computing kth roots modulo m. - Ch.18. Powers, roots and "Unbreakable" codes. - Ch.19. Euler's Phi function and sums of divisors. - Ch.20. Powers modulo p and primitive roots. - Ch.21. Primitive roots and indices. - Ch.22. Squares modulo p. - Ch.23. Is-1a square Modulo p?Is 2?. - Ch.24. Quadratic reciprocity. - Ch.25. Which primes are sums of two squares? - Ch.26. Which numbers are sums of two squares?. - Ch.27. The equation X4+Y4+Z4. - Ch.28. Square-triangular number revisited. - Ch.29. Pell's equation.

...This book will lead you through the groves wherein lurk some of the brightest flowers of number theory, as it simultaneously encourages you to investigate, analyze, conjecture, and ultimate prove your own beautiful number theoritics results. - Preface