Lectures:
Divisibility on N and Z, the greatest common divisor, Euclidean algorithm,
Canonical decomposition,
The set of prime numbers — basic knowledge of the layout to the axis,
Prime-counting function, Tschebyshev inequality, the prime number theorem and Bertrand's postulate,
Asymptotic density of sets,
Congruence relation on Z,
Linear congruences,
Operation on Zn,
Euler's totient function,
Euler-Fermat's last theorem,
Miller-Rabin primality test,
RSA algorithm.
Practices
Properties of the divisibility on N and Z, Euclid's algorithm,
Link of the canonical decomposition algorithm with the greatest common divisor and least common multiple,
Presence of the prime numbers in arithmetical sequences and g-adic expansions of numbers,
Eratosthenes sieve,
Determining the densities of sets, asymptotic density of the set of prime numbers, Properties of congruence relation,
Solving of linear congruences,
Z_p field, Wilson's theorem,
The value of the Euler's function,
Examples on Fermat's primality test and Carmichael's numbers,
Examples on the Miller-Rabin primality test,
Examples on RSA algorithm
Divisibility on N and Z, the greatest common divisor, Euclidean algorithm,
Canonical decomposition,
The set of prime numbers — basic knowledge of the layout to the axis,
Prime-counting function, Tschebyshev inequality, the prime number theorem and Bertrand's postulate,
Asymptotic density of sets,
Congruence relation on Z,
Linear congruences,
Operation on Zn,
Euler's totient function,
Euler-Fermat's last theorem,
Miller-Rabin primality test,
RSA algorithm.
Practices
Properties of the divisibility on N and Z, Euclid's algorithm,
Link of the canonical decomposition algorithm with the greatest common divisor and least common multiple,
Presence of the prime numbers in arithmetical sequences and g-adic expansions of numbers,
Eratosthenes sieve,
Determining the densities of sets, asymptotic density of the set of prime numbers, Properties of congruence relation,
Solving of linear congruences,
Z_p field, Wilson's theorem,
The value of the Euler's function,
Examples on Fermat's primality test and Carmichael's numbers,
Examples on the Miller-Rabin primality test,
Examples on RSA algorithm