Category:Number Theory
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This category contains results about Number Theory.
Definitions specific to this category can be found in Definitions/Number Theory.
Number theory is the branch of mathematics which studies the properties of the natural numbers.
Subcategories
This category has the following 200 subcategories, out of 247 total.
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- 0.999...=1 (6 P)
A
- Ackermann Functions (2 P)
- Aliquot Sums (2 P)
- Amicable Triplets (4 P)
- Aurifeuillian Factorizations (3 P)
B
- Beatty Sequences (10 P)
- Bernoulli Polynomials (3 P)
- Bertrand-Chebyshev Theorem (4 P)
- Bézout's Identity (12 P)
C
- Class Field Theory (empty)
- Collatz Conjecture (7 P)
- Computational Number Theory (empty)
- Continued Square Roots (empty)
- Cyclic Numbers (1 P)
D
- Digital Roots (6 P)
- Dimensional Analysis (2 P)
- Diophantine m-Tuples (2 P)
- Dirichlet Convolution (8 P)
- Dismal Arithmetic (empty)
- Division Theorem (24 P)
- Double Factorials (1 P)
E
- Elliptic Curves (1 P)
F
- Farey Sequence (2 P)
- Fermat Quotients (2 P)
- Fermat's Last Theorem (3 P)
- Fermat's Little Theorem (13 P)
- Fleenor-Heronian Triangles (1 P)
G
- Goldbach Conjecture (6 P)
H
- Harmonic Mean (5 P)
- Harmonic Sequences (1 P)
- Hensel's Lemma (14 P)
- Hilbert-Waring Theorem (29 P)
- Hyperoperation (5 P)
I
- Integer Sequences (2 P)
- Integral Ideals (4 P)
- Interesting Numbers (empty)
K
- Kummer Theory (empty)
L
- Locker Problem (3 P)
M
- Mills' Theorem (4 P)
- Multinomial Coefficients (2 P)
- Möbius Function (8 P)
N
- Number Fields (6 P)
O
- Oesterlé-Masser Conjecture (5 P)
P
- Pandigital Fractions (27 P)
- Pell Numbers (5 P)
- Penholodigital Integers (10 P)
- Permanents (1 P)
- Prime Gaps (11 P)
- Prime Triplets (1 P)
- Prime-Counting Function (6 P)
- Primitive Prime Factors (1 P)
- Product of Proper Divisors (1 P)
Q
- Quadratic Irrationals (4 P)
- Quasiperfect Numbers (3 P)
R
- Ramanujan-Nagell Equation (2 P)
- Rising Factorials (14 P)
S
- Signum Function (5 P)
- Simultaneous Linear Congruences (empty)
Pages in category "Number Theory"
The following 178 pages are in this category, out of 178 total.
1
A
C
- Casting Out 9s
- Catalan's Conjecture
- Characteristic Function of Square-Free Integers is Multiplicative
- Chen's Theorem
- Chinese Remainder Theorem
- Collatz Conjecture
- Commensurability is Transitive
- Completely Additive Function is Additive
- Completely Multiplicative Function is Multiplicative
- Congruence Modulo 3 of Power of 2
- Congruence of Sum of Digits to Base Less 1
- Constant to Power of Number of Distinct Prime Divisors is Multiplicative Function
- Definition:Continued Square Root
- Continuum Property implies Well-Ordering Principle
- Coprimality Criterion
- Cube Root of 2 is Irrational
- Cyclic Permutations of 5-Digit Multiples of 41
D
E
- Eisenstein Integers form Integral Domain
- Eisenstein's Lemma
- Equality of Integers to the Power of Each Other
- Equivalence of Definitions of Second Chebyshev Function
- Euclidean Algorithm
- Euler's Pentagonal Numbers Theorem
- Euler's Product form of Riemann Zeta Function
- Euler's Sum of Powers Conjecture
- Euler's Theorem
- Euler's Theorem/Corollary 1
- Exact Form of Prime-Counting Function
- Existence of Number to Power of Prime Minus 1 less 1 divisible by Prime Squared
- Existence of Prime-Free Sequence of Natural Numbers
- Existence of q for which j - qk is Positive
- Existence of Rational Powers of Irrational Numbers
F
G
H
I
- Infinite Number of Primes of form 4n - 1
- Integer as Sum of Seven Positive Cubes
- Integer as Sum of Three Odd Squares
- Integer Less One divides Power Less One
- Integer Less One divides Power Less One/Corollary
- Integer Less One divides Power Less One/Corollary/Converse
- Integer to Power of Multiple of Order
- Integer to Power of Multiple of Order/Corollary
- Integer to Power of p-1 over 2 Modulo p
- Integer to Rational Power is Irrational iff not Integer or Reciprocal
- Integers as Sum of Three Pairwise Coprime Integers
- Integers Representable as Product of both 3 and 4 Consecutive Integers
- Integers with Primitive Roots
- Integral Multiple of an Algebraic Number
- Irrationality of Logarithm
L
- Lagrange's Theorem (Number Theory)
- Largest Mutually Coprime Subset of Initial Segment of Natural Numbers
- Largest Prime Factor of n squared plus 1
- Length of Reciprocal of Product of Powers of 2 and 5
- Lifting The Exponent Lemma
- Liouville Numbers are Irrational
- Liouville's Theorem (Number Theory)
- Liouville's Theorem (Number Theory)/Corollary
- Local Maxima of Number of Goldbach Decompositions
- Locker Problem
- Lucas' Theorem
- Lucas' Theorem/Corollary
N
- Natural Number is Divisor or Multiple of Divisor of Another
- Non-Zero Integer has Finite Number of Divisors
- Number of Bits for Decimal Integer
- Number of Digits in Number
- Number of Digits to Represent Integer in Given Number Base
- Number of Multiples less than Given Number
- Number Plus One divides Power Plus One iff Odd
- Numbers Divisible by Sum and Product of Digits
- Numbers Equal to Sum of Squares of Digits
- Numbers Not Expressible as Sum of no more than 5 Squares of Composite Numbers
- Numbers not Sum of Square and Prime
- Numbers whose Cyclic Permutations of 3-Digit Multiples are Multiples
O
P
- Positive Integer is Sum of Consecutive Positive Integers iff not Power of 2
- Positive Rational Number as Power of Number with Power of Itself
- Power Function is Completely Multiplicative/Integers
- Power of Sum Modulo Prime
- Power of Sum Modulo Prime/Corollary
- Prime Divisors of Cyclotomic Polynomials
- Prime Power of Sum Modulo Prime
- Prime Power of Sum Modulo Prime/Corollary
- Primes of form Power plus One
- Primitive Root is Generator of Reduced Residue System
- Principle of Mathematical Induction
- Product of Integers of form 4n + 1
- Product of Sums
- Product of Sums/Corollary
- Product of Three Consecutive Integers is never Perfect Power
R
- Ramanujan's Infinite Nested Roots
- Rational Number as Power of Number with Itself
- Rational Square Root of Integer is Integer
- Real Logarithm is Completely Additive
- Recurring Parts of Multiples of One Thirteenth
- Recurring Parts of Multiples of Reciprocal of 53
- Richert's Theorem
- Riemann Hypothesis implies Odd Number is Sum of at most 5 Primes
- Riemann Zeta Function and Prime Counting Function
- User:Robkahn131/Sandbox
S
- Set of Divisors of Integer
- Set of Integers Bounded Above by Integer has Greatest Element
- Set of Integers Bounded Above has Greatest Element
- Set of Integers Bounded Below has Smallest Element
- Set of Successive Numbers contains Unique Multiple
- Sets of 4 Integers a, b, c, d for which Every Integer is in form ax^2 + by^2 + cz^2 + du^2
- Signum Complement Function on Natural Numbers as Characteristic Function
- Signum Function on Integers is Extension of Signum on Natural Numbers
- Signum Function on Natural Numbers as Characteristic Function
- Smallest n for which 2^n-3 is Divisible by n
- Smallest Positive Integer not of form +-4 mod 9 not representable as Sum of Three Cubes
- Square of Quadratic Gauss Sum
- Squares Ending in 5 Occurrences of 2-Digit Pattern
- Squares Ending in n Occurrences of m-Digit Pattern
- Squares Ending in n Occurrences of m-Digit Pattern/Example
- Structure of Recurring Decimal
- Sum of Odd Positive Powers
- Sum of Reciprocals of Divisors equals Abundancy Index
- Sum of Reciprocals of Primes is Divergent/Lemma
- Sum of two Fourth Powers cannot be Fourth Power
- Sum Over Divisors Equals Sum Over Quotients