Introduction to Number Theory

1. The Factorization of Integers.- 2. Congruences.- 3. Quadratic Residues.- 4. Properties of Polynomials.- 5. The Distribution of Prime Numbers.- 6. Arithmetic Functions.- 7. Trigonometric Sums and Characters.- 8. On Several Arithmetic Problems Associated with the Elliptic Modular Function.- 9. The Prime Number Theorem.- 10. Continued Fractions and Approximation Methods.- 11. Indeterminate Equations.- 12. Binary Quadratic Forms.- 13. Unimodular Transformations.- 14. Integer Matrices and Their Applications.- 15. p-adic Numbers.- 16. Introduction to Algebraic Number Theory.- 17. Algebraic Numbers and Transcendental Numbers.- 18. Waring’s Problem and the Problem of Prouhet and Tarry.- 19. Schnirelmann Density.- 20. The Geometry of Numbers.