Number Theory

This course gives an introduction to elementary number theory. Topics included are: greatest common divisor, Euclidean algorithm, linear diophantine equations, elementary prime number theory, linear congruences, Chinese remainder theorem, Fermat's little theorem, Euler's phi-function, Euler's theorem with application to cryptography, Wilson's theorem. Additional topics that may change from year to year may include number theoretical functions, primitive roots, quadratic reciprocity, Fermat's last theorem for n = 4, continued fractions, rational approximations, and Pell's equation.

1. Knowledge. The student is familiar with basic concepts in elementary number theory as specified under "Academic content".

2. Skills. The student is able to apply the theoretical knowledge to solve concrete problems. This includes being able to apply Euclid's division algorithm, solve diophantine equations and (systems of) linear congruences, encryption and decryption of messages in given RSA-systems. The student is able to write simple mathematical proofs.

3. General competence. The student recognizes the historical timeline of number theory and its relevance in modern information technology.

Exercises and written final examination. Physical or digital gatherings (agreed upon at the start of the semester with the students). Parts of this course can be taught in English.