A friendly introduction to number theory

For 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.

Cover -- 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 Revi…