11Axx Elementary number theory
This subtopic studies elementary number theory, including divisibility, congruences, primes, and the basic arithmetic tools that underlie much of analytic and algebraic number theory.
Specific topics
11A05 Multiplicative structure; Euclidean algorithm
Overview
11A05 examines multiplicative structure; euclidean algorithm within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Multiplicative structure; Euclidean algorithm (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for multiplicative structure; euclidean algorithm
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11A07 Congruences; primitive roots; residue systems
Overview
11A07 examines congruences; primitive roots; residue systems within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Congruences; primitive roots; residue systems (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for congruences; primitive roots; residue systems
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11A15 Power residues, reciprocity
Overview
11A15 examines power residues, reciprocity within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Power residues, reciprocity (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for power residues, reciprocity
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11A25 Arithmetic functions; related numbers; inversion formulas
Overview
11A25 examines arithmetic functions; related numbers; inversion formulas within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Arithmetic functions; related numbers; inversion formulas (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for arithmetic functions; related numbers; inversion formulas
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11A41 Primes
Overview
11A41 examines primes within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Primes (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for primes
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11A51 Factorization; primality
Overview
11A51 examines factorization; primality within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Factorization; primality (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for factorization; primality
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11A55 Continued fractions
Overview
11A55 examines continued fractions within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Continued fractions (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for continued fractions
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11A63 Radix representation; digital problems
Overview
11A63 examines radix representation; digital problems within elementary number theory. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Radix representation; digital problems (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for radix representation; digital problems
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks