Introduction to number theory

1. The Factorization of Integers.- 1.1 Divisibility.- 1.2 Prime Numbers and Composite Numbers.- 1.3 Prime Numbers.- 1.4 Integral Modulus.- 1.5 The Fundamental Theorem of Arithmetic.- 1.6 The Greatest Common Factor and the Least Common Multiple.- 1.7 The Inclusion-Exclusion Principle.- 1.8 Linear Indeterminate Equations.- 1.9 Perfect Numbers.- 1.10 Mersenne Numbers and Fermat Numbers.- 1.11 The Prime Power in a Factorial.- 1.12 Integral Valued Polynomials.- 1.13 The Factorization of Polynomials.- Notes.- 2. Congruences.- 2.1 Definition.- 2.2 Fundamental Properties of Congruences.- 2.3 Reduced Residue System.- 2.4 The Divisibility of 2p-1-1 by p2.- 2.5 The Function ?(m).- 2.6 Congruences.- 2.7 The Chinese…