Syllabus

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Faculty: Faculty of Engineering and Natural Sciences

Semester: Fall 2025-2026

Course: Elementary Number Theory - MATH 317

Classroom: FENS-L035,FENS-L062

Level of course: Undergraduate

Course Credits: SU Credit:3.000, ECTS:6, Basic:6

Prerequisites: MATH 102 and MATH 201

Corequisites:

Course Type: Lecture

Divisibility, prime numbers, congruences, quadratic residues, arithmetic functions, the Riemann Zeta function.

1.	Prove simple facts about divisibility, greatest common divisors, least common multiples,
2.	Understand the Euclidean Algorithm
3.	Understand the Fundamental Theorem of Arithmetic
4.	Solve linear Diophantine equations and linear congruences
5.	Understand and apply Fermat's Little Theorem
6.	Determine Euler Phi Function and prove simple facts about Euler Phi Function
7.	Prove simple facts about primitive roots
8.	Apply the Law of Quadratic Reciprocity
9.	Show simple facts about quadratic residues
10.	Decide if an integer can be written as a Sum of Squares
11.	Apply standard proof methods like mathematical induction, direct and indirect proofs
12.	Present simple proofs in a precise and formally correct way.

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