UsefulLinks
Mathematics
Number Theory
1. Foundations of Number Theory
2. Divisibility Theory
3. Prime Numbers and Factorization
4. Greatest Common Divisor and Least Common Multiple
5. Modular Arithmetic and Congruences
6. Classical Theorems in Number Theory
7. Arithmetic Functions
8. Diophantine Equations
9. Quadratic Residues and Reciprocity
10. Prime Number Theory
11. Continued Fractions
12. Elementary Analytic Number Theory
13. Cryptographic Applications
14. Advanced Topics and Connections
11.
Continued Fractions
11.1.
Basic Theory
11.1.1.
Definition and Notation
11.1.2.
Finite Continued Fractions
11.1.3.
Infinite Continued Fractions
11.1.4.
Convergence Properties
11.2.
Rational Numbers
11.2.1.
Continued Fraction Representation
11.2.2.
Uniqueness and Algorithms
11.2.3.
Euclidean Algorithm Connection
11.3.
Irrational Numbers
11.3.1.
Continued Fraction Expansions
11.3.2.
Periodic Continued Fractions
11.3.3.
Quadratic Irrationals
11.4.
Convergents
11.4.1.
Definition and Computation
11.4.2.
Properties of Convergents
11.4.3.
Best Rational Approximations
11.4.4.
Error Estimates
11.5.
Applications
11.5.1.
Solving Pell's Equation
11.5.2.
Calendar Problems
11.5.3.
Musical Scales
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10. Prime Number Theory
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12. Elementary Analytic Number Theory