**
Math 346 SPRING 2017, List of lectures
**

On this page I will post content of all lectures with reference to the
book. All handouts also will be posted here.
Monday, April 3: Overview. Chapter 0.
Wednesday, April 5: The Greatest Common Divisor and Least Common Multiple.
Section 1.1.
Here is homework!
Friday, April 7: The Division Algorithm. The Euclidean Algorithm.
Sections 1.2-1.3.
Monday, April 10: Linear combinations. Section 1.4. We will have QUIZ on
Friday!!!
Wednesday, April 12: More on linear combinations. Section 1.4.
New homework!
Friday, April 14: Congruences. Section 1.5.
Here are solutions to the quiz.
Monday, April 17: Mathematical Induction. Section 1.6.
We will have QUIZ on Friday!!!
Wednesday, April 19: Strong Principle of Induction. Primes and
composite numbers. Why uniqueness of prime decomposition is not obvious.
Sections 2.1-2.2.
New homework!
Friday, April 21: The Fundamental Theorem of Arithmetic.
Sections 2.2-2.4.
Here are solutions to the quiz.
Monday, April 24: Any composite number has a divisor
less than its square root. Sections 2.4-2.5.
We will have QUIZ on Friday!!!
Wednesday, April 26: The set of primes is infinite. The digit theorem.
A formula for the number of divisors. The sum of divisors. Sections 2.6-3.1, 3.3.
New homework!
Friday, April 28: Perfect numbers. Mersenne primes. Sections 3.3-3.4.
Here are solutions to the quiz.
Monday, May 1: Fermat primes. Euler phi function. Sections 3.4-3.5.
We will have QUIZ on Friday!!!
Wednesday, May 3: Solving congruences. Linear congruences. Section 4.1.
New homework!
Friday, May 5: More on linear congruences. Section 4.1.
Here are solutions to the quiz.
Monday, May 8: The Chinese Remainders Theorem. Section 4.2.
We will have MIDTERM on Friday!!!
Please find here practice problems for midterm.
Wednesday, May 10: Euler and Fermat theorem. Section 4.3.
Here are the solutions to practice midterm.
New homework!
Friday, May 12: MIDTERM.
Here are solutions.
Monday, May 15: Order of a modulo b. Section 4.3.
We will have QUIZ on Friday!!!
Wednesday, May 17: Primality testing. Section 4.4.
New homework!
Friday, May 19: RSA. Section 4.5.
Here are (now corrected!) solutions to the quiz.
Monday, May 22: Higher degree congruences. Section 5.1. We will have
QUIZ on Friday!!!
Wednesday, May 24: Congruences with Prime Power Moduli. Section 5.2.
New homework!
Friday, May 26: Quadratic Residues. Section 5.3.
Here are solutions to the quiz.
Monday, May 29: no classes, Memorial Day.
Wednesday, May 31: Euler criterion for quadratic residues. Legendre symbol.
Section 5.3. We will have QUIZ (covering Sections 5.1-5.4)
on Monday!!!
Friday, June 2: Gauss Lemma. Computation of the Legendre symbol (2/p).
Section 5.4.
Last homework (due next Friday)!
Monday, June 5: The Legendre symbol (3/p). The Pepin test. Sections 5.4
and 4.4.
Please find here practice problems for
the final.
Here are solutions to the quiz.
Wednesday, June 7: The quadratic reciprocity. Sections 5.4-5.5.
Friday, June 9: Jacobi symbol. Flipping a coin over the phone. Section 5.5.
Please find here solutions for the
practice problems.
END