1.1. Mathematical induction

1.2. The binomial theorem

2.1. Early number theory

2.2. Division algorithm

2.3. Greatest common divisors

2.4. The Euclidean algorithm

2.5. Linear Diophantine equations

3.1. Fundamental Theorem of Arithmetic;

       Irrationality of square root of 2

3.2. The Sieve of Eratosthenes;

      Infinitude of primes

4.2. Congruences

4.3. Binary and decimal representations;

      division tests

Review

Test 1 (over 1.1-2.5)

4.4. Linear congruences and the Chinese Remainder Theorem

5.2.  Fermat's Little Theorem

5.4.  The Fermat Factorization Method

6.1.  The number and sum of divisors

7.2.  The Euler phi function

7.3.  Euler's Theorem

Review

Test 2  (over 3.1-5.2)

8.1. The order of an integer modulo n

8.2.  Primitive roots

10.1. Cryptography

11.2. Perfect numbers

12.1. Pythagorean triples

12.2. Fermat's Last Theorem

Review

Test 3 (over 6.1-11.2)

15.2. Finite continued fractions

15.3. Infinite continued fractions

9.1. Euler's criterion

9.2. Legendre symbols

9.3. Quadratic reciprocity

Review

Final Exam (comprehensive)