18.781 | Spring 2012 | Undergraduate

# Theory of Numbers

## Calendar

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
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 Brahmagupta-Pell Equation
24 Four Squares Theorem Pset 9 due
25 Pythagorean Triples, Fermat Descent
26 Rational Points on Conics