Discrete Mathematics 2

Learning Outcomes

  1. To solve linear congruence and a system of linear congruences.
  2. Solve some of the polynomial and exponential congruences via prime roots.
  3. Examine the solution existence of quadratic congruence by virtue of the Jacobi symbol.
  4. Solve some basic diophantine equations.
  5. Compute in finite fields.
  6. Apply number theory and group theory in public key cryptography.

Forms of Teaching


Independent assignments


Week by Week Schedule

  1. The Euclidean algorithm; Prime numbers.
  2. Linear congruences; The Chinese Remainder Theorem.
  3. Euler's phi-function.
  4. Primitive roots; Solving some polynomial congruences.
  5. The Legendre symbol; The Jacobi symbol.
  6. The Quadratic Reciprocity Law.
  7. Linear Diophantine equations; Pythagorean triples; Pell's equation.
  8. Midterm exam.
  9. Semigroups and groups.
  10. Rings and fields.
  11. Finite fields.
  12. Introduction to cryptography.
  13. Symmetric cryptography.
  14. The RSA cryptosystem; Public-key cryptography.
  15. Final exam.

Study Programmes

University undergraduate
Computing (study)
Elective Courses (6. semester)
Electrical Engineering and Information Technology (study)
Elective Courses (6. semester)
University graduate
Audio Technologies and Electroacoustics (profile)
Elective Courses (2. semester)
Communication and Space Technologies (profile)
Elective Courses (2. semester)
Computational Modelling in Engineering (profile)
Elective Courses (2. semester)
Computer Engineering (profile)
Elective Courses (2. semester)
Computer Science (profile)
Elective Courses (2. semester)
Control Systems and Robotics (profile)
Elective Courses (2. semester)
Data Science (profile)
Elective Courses (2. semester)
Electrical Power Engineering (profile)
Elective course (2. semester)
Electric Machines, Drives and Automation (profile)
Elective Courses (2. semester)
Electronic and Computer Engineering (profile)
Elective Courses (2. semester)
Electronics (profile)
Elective Courses (2. semester)
Information and Communication Engineering (profile)
Elective courses (2. semester)
Network Science (profile)
Elective Courses (2. semester)
Software Engineering and Information Systems (profile)
Elective Courses (2. semester)


(.), Andrej Dujella, Uvod u teoriju brojeva, https://web.math.pmf.unizg.hr/~duje/utb/utblink.pdf,
(.), K. H. Rosen: Elementary Number Theory and Its Applications, Addison-Wesley, Reading, 1993.,
(.), D. Žubrinić, Diskretna matematika, Element, 1997.,
(.), Course in Number Theory and Cryptography N. Koblitz Springer 1994,
(.), A. Baker: A Concise Introduction to the Theory of Numbers, Cambridge University Press, Cambridge, 1994.,
(.), I. Niven, H. S. Zuckerman, H. L. Montgomery: An Introduction to the Theory of Numbers, Wiley, New York, 1991.,
(.), A. Baker: A Comprehensive Course in Number Theory, Cambridge University Press, Cambridge, 2012.,
(.), Cryptography. Theory and Practice D. R. Stinson CRC Press 2002,


ID 183494
  Summer semester
L3 English Level
L1 e-Learning
45 Lectures
0 Exercises
4 Laboratory exercises
0 Project laboratory

Grading System

Very Good