- understand the concept of divisibility and be able to carry out proofs of simple related results
- know the concept of prime numbers and proofs for the infinity of the set of prime numbers
- know interesting properties of primes and related open questions
- have skills in dealing with the GCD and the application of the Euclidean algorithm
- be able to compute finite continued fraction expansions
- be able to solve linear Diophantine equations
- be able to compute digit-expansions of natural numbers
- be able to deal with congruences and remainder classes modulo m
- be familiar with fundamental algebraic structures
- know the algebraic structure of the ring of integers modulo m
- be able to derive simple divisibility rules in connection with digit-expansions
- know and understand the group of primitive residue classes modulo m
- know Euler’s totient function and to be able to prove simple related properties
- know criteria for the solvability of systems of linear congruences
- know and be able to execute RSA crypto systems
- be able to apply the method of binary exponentiation
- know the classical questions of constructions with compass and ruler and the relation of these questions to number theory
- know the concept of quadratic field extensions
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Divisibility of integers, prime numbers, GCD, Euclidean algorithm, Diophantine equations, Pythagorean triples, digit expansions, congruences and residue classes, application: perpetual calendar, algebraic structures (ring, integral domain, field), prime residue class group, Euler's totient function, RSA cryptosystem, constructions with compass and ruler
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