An introductory guide to elementary number theory for advanced undergraduates and graduates.
Table of ContentsIntroduction; 1. Greatest common divisors; 2. Unique factorization; 3. Linear diophantine equations; 4. Congruences; 5. Linear congruences; 6. The Chinese Remainder Theorem; 7. Fermat's Theorem; 8. Wilson's Theorem; 9. The number of divisors of an integer; 10. The sum of the divisors of an integer; 11. Amicable numbers; 12. Perfect numbers; 13. Euler's Theorem and function; 14. Primitive roots and orders; 15. Decimals; 16. Quadratic congruences; 17. Gauss's Lemma; 18. The Quadratic Reciprocity Theorem; 19. The Jacobi symbol; 20. Pythagorean triangles; 21. x4+y4≠z4; 22. Sums of two squares; 23. Sums of three squares; 24. Sums of four squares; 25. Waring's Problem; 26. Pell's Equation; 27. Continued fractions; 28. Multigrades; 29. Carmichael numbers; 30. Sophie Germain primes; 31. The group of multiplicative functions; 32. Bounds for ∏(x); 33. The sum of the reciprocals of the primes; 34. The Riemann Hypothesis; 35. The Prime Number Theorem; 36. The abc conjecture; 37. Factorization and testing for primes; 38. Algebraic and transcendental numbers; 39. Unsolved problems; Index; About the author.
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