Materials Covered and Suggested Readings, Week 1, 1/10--1/14

In the first week, we will discuss some basic properties of congruences. We will not follow the order of presentation of Rosen's book, in order to get to some interesting points as quickly as possible. The proofs we give may be different from those in Rosen's book. We will follow the organization of Rosen's book more closely later. Rosen's book emphasizes computation from the beginning, and we will not discuss the computational aspects in the first week.

• Please read the statement of the Fundamental Theorem of Arithmetic (Theorem 3.15 in Rosen)
• Congruences: Definition and first properties (sections 4.1 and 4.2 of Rosen)
  
• Fermat's Little Theorem (section 6.1 of Rosen)
  
• The Chinese Remainder Theorem (section 4.3 of Rosen)
• Polynomial congruence equations and Hensel's Lemma (section 4.4 of Rosen)