https://studiegids.vu.nl/en/courses/2025-2026/X_400632The student is able to perform basic number theoretic calculations (including congruence arithmetic, primes, continued fractions algorithm, arithmetic functions, Jacobi symbols, constructions of rational points on conic sections and cubic curves from other rational points) to solve concrete problems.The student knows some central applications, open problems, and related directions in number theory (including factorization, cryptography, abc-conjecture, Mason-Stothers theorem) and can analyze their consequences for specific situations.The student knows fundamental number theoretic concepts and theorems (including primitive roots, quadratic reciprocity, Diophantine equations, some algebraic number theory, continued fractions) and can solve problems/create proofs about and with those in explicit situations.The following subjects will be treated:integers, primes, prime distributioncongruences, primitive rootsprimality tests, factorizationpublic key cryptographyquadratic reciprocityDiophantine equations, abc-conjecturealgebraic numbers, algebraic integerscontinued fractionsNext to a theoretical approach, practical/algorithmic aspects will also be covered.Lectures and exercise sessions (‘werkcolleges’), both 2 hours per week.Homework assignments (25%) and a final written exam (75%). Extra rule: the grade for the final exam must be at least 5.0 in order to pass the course. The re-examination possibility consists of a written exam whose mark determines the final grade in principle for 100%.Lecture notes, the relevant literature will be made available online.Third year BSc Mathematics.Basic knowledge of groups, rings, and fields is essential.