Number Theory
Definition and Notation
Properties of GCD
GCD and Prime Factorization
Linear Combination Property
Algorithm Description
Step-by-Step Examples
Proof of Correctness
Efficiency and Complexity
Variants of the Algorithm
Bézout's Identity
Finding Linear Combinations
Applications to Modular Arithmetic
Properties of LCM
LCM and Prime Factorization
Relationship Between GCD and LCM
Definition of Coprimality
Properties of Relatively Prime Numbers
Characterizations of Coprimality
Applications in Number Theory
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3. Prime Numbers and Factorization
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5. Modular Arithmetic and Congruences