A Friendly Introduction to Number Theory by Joseph Silverman

Book 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 k-th Roots Modulo m 18. Powers, Roots, and “Unbreakable” Codes 19. Primality Testing and Carmichael Numbers 20. Squares Modulo p 21. Is -1 a Square Modulo p? Is 2? 22. Quadratic Reciprocity 23. Proof of Quadratic Reciprocity 24. Which Primes Are Sums of Two Squares? 25. Which Numbers Are Sums of Two Squares? 26. As Easy as One, Two, Three 27. Euler’s Phi Function and Sums of Divisors 28. Powers Modulo p and Primitive Roots 29. Primitive Roots and Indices 30. The Equation X4 + Y4 = Z4 31. Square–Triangular Numbers Revisited 32. Pell’s Equation 33. Diophantine Approximation 34. Diophantine Approximation and Pell’s Equation 35. Number Theory and Imaginary Numbers 36. The Gaussian Integers and Unique Factorization 37. Irrational Numbers and Transcendental Numbers 38. Binomial Coefficients and Pascal’s Triangle 39. Fibonacci’s Rabbits and Linear Recurrence Sequences 40. Oh, What a Beautiful Function 41. Cubic Curves and Elliptic Curves 42. Elliptic Curves with Few Rational Points 43. Points on Elliptic Curves Modulo p 44. Torsion Collections Modulo p and Bad Primes 45. Defect Bounds and Modularity Patterns 46. Elliptic Curves and Fermat’s Last Theorem 47. The Topsy-Turvy World of Continued Fractions [online] 48. Continued Fractions and Pell’s Equation [online] 49. Generating Functions [online] 50. Sums of Powers [online]

About this book :-
"A Friendly Introduction to Number Theory" by Joseph H. Silverman is a welcoming and engaging entry point into "number theory" for beginners. Written with clarity and warmth, the book assumes only basic algebra and gradually introduces readers to deeper mathematical thinking. Through simple examples and patterns, it helps students develop intuition while learning how mathematicians approach problems and ideas. The book focuses strongly on "proof techniques", encouraging readers to experiment, make conjectures, and justify results logically. Core topics include "divisibility", "congruences", prime numbers, and modular arithmetic, with natural connections to real-world ideas such as "cryptography". Rather than presenting results as facts to memorize, Silverman guides readers to discover why statements are true, building confidence and problem-solving skills along the way. Ideal for undergraduates, self-learners, and first courses in number theory, this book balances rigor with accessibility. Its friendly tone, thoughtful exercises, and emphasis on mathematical thinking make it especially effective for students transitioning from computational math to abstract reasoning. By the end, readers gain both a solid foundation in "number theory" and a deeper appreciation for how mathematical ideas are explored, tested, and proven.

Book Detail :-
Title: A Friendly Introduction to Number Theory by Joseph Silverman
Publisher: Pearson
Year: 2012
Pages: 456
Type: PDF
Language: English
ISBN-10 #: 0134689461
ISBN-13 #: 978-0134689463
License: External Educational Resource
Amazon: Amazon

About Author :-
The author Joseph H. Silverman is an American mathematician and professor at "Brown University", widely known for his work in "number theory" and arithmetic geometry. He earned his PhD from Harvard University and has made major contributions to elliptic curves and Diophantine equations. Silverman is also respected for writing clear, student-friendly mathematics textbooks. His work, "A Friendly Introduction to Number Theory", introduces core ideas such as "primes", "modular arithmetic", and Diophantine problems using intuitive explanations and engaging examples.

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