Number Theory: Greatest Common Divisor and Prime Factorization

Related lectures (28)

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Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

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

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

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

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

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

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

Introduces Cartesian product and induction for proofs using integers and sets.