Elementary Number Theory I
Math 365 - Fall 2017

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Exams

Midterm 1 (% 30 - November 6, Monday)

Midterm 2 (% 30 - December 4, Monday)

Final (% 40 - January 8, Monday)

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Course Outline

The Division Algorithm, The Greatest Common Divisor.

The Euclidean Algorithm, The Diophantine Equation ax+by=c.

The Fundamental Theorem of Arithmetic, Primes and Their Distribution.

Basic Properties of Congruences, Special Divisibility Tests.

Linear Congruences, Chinese Remainder Theorem.

Fermat's and Wilson's Theorems.

Number-Theoretic Functions tau and sigma.

The Mobius Inversion Formula

The Greatest Integer Function

Euler's phi-Function, Euler's Theorem.

Properties of phi-Function, An Application to Cryptography

Primitive Roots.

The Quadratic Reciprocity Law.

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Course Objectives and Learning Outcomes

This is a basic number theory course which deals with division algorithm, prime numbers and their primitive roots, the theory of congruences, quadratic reciprocity law and number theoretic functions. The students who succeed in this course

will be able to use the division algorithm,

will be able to comprehend the primes numbers, their distributions and the notion of congruences,

will be able to define number-theoretic functions and understand their applications in cryptography,

will be able to identify primitive roots and indices.

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Course Policy

Attendance will be taken and if your attendance is less than %70, you will not be able to take the final exam and receive the NA grade.

Only one make-up examination will be offered. The excuse for not attending an examination must be proved with documents. The make-up examination will take place shortly after the final exam.