SES #  TOPICS  KEY DATES 

1  Introduction, Diophantine Equations, Divisibility, GCD  
2  Euclidean Algorithm, Primes  Pset 1 out 
3  Binomial Coefficients, Congruences  
4  Fermat, Euler, Wilson, Linear Congruences  Pset 1 due, Pset 2 out 
5  Linear Congruences, Chinese Remainder Theorem, Algorithms  Pset 2 due, Pset 3 out 
6 
Primality, Factoring, RSA, Hensel’s Lemma 

7  Congruences mod Primes, Order, Primitive Roots  Pset 3 due, Pset 4–1 out 
8  Primitive Roots (Prime Powers), Index Calculus  
9  Midterm 1  Pset 4–2 out 
10  Quadratic Residues, Quadratic Reciprocity  
11  Jacobi Symbol, Computation, Zolotareff’s Definition  Pset 4 due 
12  Square Roots, Tonelli’s Algorithm, Number of Consecutive Pairs of Squares mod p  Pset 5 out 
13  Cyclotomic Polynomials, Primes Congruent to 1 mod n  
14  Arithmetic Functions  
15  Mobius Inversion Formula, Zeta Functions  Pset 5 due, Pset 6 out 
16  Linear Recurrences  
17  Generating Functions  Pset 6 due, Pset 7 out 
18  Midterm 2  
19  More on Generating Functions, Two Squares Theorem  
20  Continued Fractions I  Pset 7 due, Pset 8 out 
21  Continued Fractions II: Inequalities  
22  Periodic Continued Fractions, Quadratic Irrationalities  Pset 8 due, Pset 9 out 
23  BrahmaguptaPell Equation  
24  Four Squares Theorem  Pset 9 due 
25  Pythagorean Triples, Fermat Descent  
26  Rational Points on Conics 
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