Lectures related to Number Theory: GCD and LCM

Covers GCD, LCM, and the Euclidean algorithm for efficient computation.

Introduces greatest common divisor, prime factorization, and the Euclidean Algorithm.

Explores prime numbers, coprime integers, and their properties in number theory.

Covers prime numbers, unique decomposition of natural numbers into prime factors, and practical implications for calculations.

Delves into the complexity of factoring polynomials and the implications for security.

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.

Explores Gaussian integers, prime factorization, and number theory concepts related to prime numbers.

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

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

Covers Shor's factoring algorithm, aiming to find integer factors efficiently using quantum computation.

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.

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

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Covers the basics of Shor's algorithm for factoring integers and the steps involved in the quantum algorithm.

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Covers function composition and integers, including properties and examples.

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

Introduces integer numbers, well-ordering, induction principles, GCD, LCM, and Bezout's theorem.

Covers Lenstra's Algorithm for integer factorization, which efficiently computes prime factors of an integer.

Explores cosets in commutative groups, Lagrange theorem, and integer factorization.