Lectures related to Number Theory: Division

Covers number theory, division, remainder, congruence, prime numbers, integer representation, and the Euclidean algorithm.

Explores the history and concepts of Number Theory, including divisibility and congruence relations.

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Covers the Euclidean algorithm for GCD calculation and algorithmic complexity analysis.

Introduces modulo arithmetic, Euclid's algorithm, and congruence in number theory.

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

Introduces number theory and its essential applications in cryptography.

Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Explains the conversion between decimal and fractional writing, including division with remainder and a trick for periodic numbers.

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Covers the properties of division in integers and the relationship between divisibility and unique quotients.

Explores the Chinese remainder theorem, systems of congruences, and Euclidean domains in integer numbers and polynomial rings.

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.

Explores total order broadcast and its equivalence to consensus in reliable systems.

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.