North Carolina State University, Department of Mathematics

TEXT: Elementary Number Theory, Fifth Edition, by David M. Burton

Jan. 9 - Mathematical Induction; The Binomial Theorem.

Jan. 11 - The Division Algorithm; The Greatest Common Divisor.

Jan. 13 - The Deophantine Linear Equations.

Jan. 18 - Prime Numbers and Their Distribution .

Jan. 20 - Basic Properties of Congruence

Jan. 23 - Divisibility Tests and Linear Congruences.

Jan. 25 - Fermat’s Theorem.

Jan. 27 -TEST I

Jan. 30 - Number – Theoretic Functions.

Feb. 1 - The Mobius Inversion Formula and The Greatest Integer Function.

Feb. 3 - Euler’s Phi-Function.

Feb. 6 - Euler’s Generalization of Fermat’s Theorem.

Feb. 8 - Some Properties of Euler’s Phi-Function.

Feb. 10 - An Application to Cryptography ( R.S.A. Application ).

Feb. 13 - The Order of an Integers Modulo n

Feb. 15 - Primitive Roots for Primers.

Feb. 17 - The Theory of Indices.

Feb. 20 - The Quadratic Reciprocity Law.

Feb. 22 - The Legender Symbol and Its Properties

Feb. 24 - TEST II

Feb. 27 - Quadratic Congruences.

Mar. 1 - Perfect Numbers.

Mar. 3 - Mersenne Primes.

Mar. 13 - Fermat’s Numbers.

Mar. 15 - The Famous Fermat’s Last Theorem.

Mar. 17 - Representation of Integers as Sums of Squares.

Mar. 20 - Fibonacci Numbers.

Mar. 22 - Certain Identities Involving Fibonacci Numbers.

Mar. 24 - Continued Fractions.

Mar. 27 - Finite Continued Fractions.

Mar. 29 - Infinite Continued Fractions and Pell’s Equation.

Mar. 31 - TEST III

Apr. 3 - Some Twentieth-Century Developments.

Apr. 5 - Primality Testing and Factorization.

Apr. 7 - The Prime Number Theorem.

Apr. 10 - How To Determine Whether a Given Integer is Prime

Apr. 12 - Recent Discovery of Agrawal, Kayal and Saxena’s Algorithm to Determine

A Given Integer is Prime or Not.

Apr. 17 - A. K. S. Theorem

Apr. 19 - Study of A. K. S. Algorithm.

Apr. 21 - TEST IV

Apr. 24, 28 and 29

We will review the material that which we have covered so far.