# Category:Proof Wanted

These are pages containing theorems which do not have a proof posted.

See the ProofWanted template.

## Pages in category "Proof Wanted"

The following 200 pages are in this category, out of 1,764 total.

(previous page) (next page)### 1

- 10 Consecutive Integers contain Coprime Integer
- 10 is Only Triangular Number that is Sum of Consecutive Odd Squares
- 1105 as Sum of Two Squares
- 12 Identical Spheres can touch One Other Sphere
- 12 Knights to Attack or Occupy All Squares on Chessboard
- 12 Pentominoes
- 1285 9-ominoes
- 132 is Sum of all 2-Digit Numbers formed from its Digits
- 159 is not Expressible as Sum of Fewer than 19 Fourth Powers
- 17 Wallpaper Groups
- 18 Pentominoes including Reflections

### 2

### 3

- 3 Configurations of 9 Lines with 3 Intersection Points on each Line
- 3 Non-Parallel Planes divide Space into 8
- 319 is not Expressible as Sum of Fewer than 19 Fourth Powers
- 333,667 is Only Prime whose Reciprocal is of Period 9
- 35 Hexominoes
- 369 Octominoes
- 399 is not Expressible as Sum of Fewer than 19 Fourth Powers
- 3^x + 4^y equals 5^z has Unique Solution

### 4

### 5

### A

- Abel-Ruffini Theorem
- Abelianization of Free Group is Free Abelian Group
- Absolute Value Equals Square Root of Square
- Absolute Value of Uniformly Convergent Product
- Adjoint of Finite Rank Operator
- Alaoglu's Theorem
- Alexander Polynomial is a Knot Invariant
- Alexandroff Extension of Rational Number Space is Sequentially Compact
- Algebra Defined by Ring Homomorphism is Algebra
- Algebraic Closure of Field is Unique
- Algebraic Numbers form Field
- Algebraically Closed Field is Perfect
- Algorithm to determine whether Polynomial Diophantine Equation has Integer Solution
- Alternating Even-Odd Digit Palindromic Prime
- Alternating Group is Simple
- Alternating Groups that are Ambivalent
- Amicable Pair/Examples/3^4 x 5 x 11 x 5281^19 x 29 x 89 (2 x 1291 x 5281^19 - 1)-3^4 x 5 x 11 x 5281^19 (2^3 x 3^3 x 5^2 x 1291 x 5281^19 - 1)
- Analytic Basis is Analytic Sub-Basis
- Angle of Tangent to Radius in Polar Coordinates
- Angles with Parallel or Perpendicular Arms are Equal or Supplementary
- Anisotropic Vector Gives Composition of Bilinear Space
- Annihilator is Submodule of Algebraic Dual
- Anomalous Cancellation on 2-Digit Numbers
- Approximate Formula for Number of Partitions
- Approximate Size of Sum of Harmonic Series
- Approximation to Power of 7 by Power of 10
- Approximations to Equilateral Triangles by Heronian Triangles
- Apéry's Theorem
- Archimedes' Limits to Value of Pi
- Are All Perfect Numbers Even?/Progress/Form
- Are All Perfect Numbers Even?/Progress/Minimum Size
- Are All Perfect Numbers Even?/Progress/Prime Factors
- Are All Triperfect Numbers Even?/Progress/Form
- Are All Triperfect Numbers Even?/Progress/Minimum Size
- Are All Triperfect Numbers Even?/Progress/Prime Factors
- Area between Radii and Curve in Polar Coordinates
- Area of Carthage
- Area of Smallest Rectangle accommodating Re-Entrant Knight's Tour
- Area of Smallest Square accommodating Re-Entrant Knight's Tour
- Arithmetic Progression of 4 Terms with 3 Distinct Prime Factors
- Arnauld's Paradox
- Arrow Paradox
- Atlas is Contained in Unique Maximal Atlas
- Automorphic Numbers with 10 Digits
- Automorphic Numbers with 5 Digits
- Automorphism Group of C Over R

### B

- Baire Characterisation Theorem
- Baire Space iff Open Sets are Non-Meager
- Banach-Steinhaus Theorem
- Barbier's Theorem
- Bases of Finitely Generated Free Module have Equal Cardinality
- Basis for Open Ordinal Topology
- Basis for Product of Metric Spaces under Chebyshev Distance
- Bendixson-Dulac Theorem
- Beppo Levi's Theorem
- Bernoulli Number in terms of Euler Numbers
- Bernoulli's Hanging Chain Problem
- Bernoulli's Theorem
- Bessel's Inequality
- Best Approximation from Below to 1 as Sum of Minimal Number of Unit Fractions
- Best Rational Approximations to Root 2 generate Pythagorean Triples
- Beta Function as Integral of Power of t by Power of 1 minus t over Power of r plus t
- Beta Function is Continuous and Positive on Positive Reals
- Big-O Notation for Sequences Coincides with General Definition
- Binet Form
- Binet's Formula for Logarithm of Gamma Function/Formulation 1
- Binet's Formula for Logarithm of Gamma Function/Formulation 2
- Binomial Form of Relation between Riemann Zeta Function and Dirichlet Eta Function
- Binomial Theorem for Negative Index and Negative Parameter
- Binomial Theorem/Extended
- Binomial Theorem/Hurwitz's Generalisation
- Body behaves as Particle under Gravitation
- Body in Free Fall moves in Parabolic Path
- Boolean Prime Ideal Theorem
- Borel-Carathéodory Lemma
- Borsuk-Ulam Theorem
- Bott-Milnor-Kervaire 1,2,4,8 Theorem
- Bounded iff Big-O of 1/Sequences
- Bounded Linear Transformation Induces Bounded Sesquilinear Form
- Bounds for Weierstrass Elementary Factors
- Brianchon's Theorem
- Brianchon's Theorem is Projective Dual to Pascal's Theorem
- Brouncker's Formula
- Brun's Theorem
- Buffon's Needle
- Burnout Height of Upward Rocket under Constant Gravity
- Burnout Velocity of Upward Rocket under Constant Gravity
- Burnside's Theorem
- Bézout's Theorem

### C

- Canonical Basis of Free Module on Set is Basis
- Canonical Homomorphism to Polynomial Ring is Ring Monomorphism
- Cantor Space is Non-Meager in Itself
- Carathéodory's Theorem (Measure Theory)
- Cardinality is Additive Function
- Cardinality of Cartesian Product/General Result
- Cardinality of Power Set of Natural Numbers Equals Cardinality of Real Numbers
- Cardinality of Set of All Mappings
- Cardinality of Set of All Mappings/Infinite Sets
- Carmichael Number has 3 Odd Prime Factors
- Carmichael's Theorem
- Cartesian Product of Unions/General Result
- Category of Finite Sets is Cartesian Closed
- Category of Posets is Cartesian Closed
- Category of Subobject Classes is Order Category
- Category of Vector Spaces is Category
- Cauchy Product of Absolutely Convergent Series
- Cavalieri's Principle
- Cavalieri's Principle/Extension
- Cayley-Menger Determinant
- Center is Characteristic Subgroup
- Center of Gravity of Cycloid
- Center of Group is Kernel of Conjugacy Action
- Central Product/Examples/D4 with D4
- Central Product/Examples/Q with Q
- Centralizer of Self-Inverse Element of Non-Abelian Finite Simple Group is not That Group
- Centralizer of Subset is Intersection of Centralizers of Elements
- Champernowne Constant is Normal
- Champernowne Constant is Transcendental
- Change of Coordinate Vector Under Change of Basis
- Change of Index Variable of Summation
- Change of Index Variable of Supremum
- Change of Lead in Prime Number Race 4n+1 vs. 4n-1
- Characterisation of UFDs
- Characteristic Function of Limit Inferior of Sequence of Sets
- Characteristic Function of Limit Superior of Sequence of Sets
- Characteristics of Pentatope
- Characteristics of Regular 4-Dimensional Polytopes
- Characterization of Bases (Hilbert Spaces)
- Characterization of Cosine Integral Function
- Characterization of Finite Rank Operators
- Characterization of Invariant Subspaces
- Characterization of Normal Operators
- Characterization of Pre-Measures
- Characterization of Projections
- Characterization of Reducing Subspaces
- Characterization of Unitary Operators
- Chen's Theorem
- Chinese Remainder Theorem/General Result 2
- Chu-Vandermonde Identity for Gaussian Binomial Coefficients
- Chu-Vandermonde Identity/Extended
- Class is Transitive iff Union is Subset
- Classification of Bounded Sesquilinear Forms
- Classification of Compact Three-Manifolds Supporting Zero-Curvature Geometry
- Classification of Compact Two-Manifolds
- Closed Extension Topology is not T3
- Closed Set of Ultraconnected Space is Ultraconnected
- Closure of Complement of Closure is Regular Closed
- Closure of Irreducible Subspace is Irreducible
- Closure of Range of Compact Linear Transformation is Separable
- Closure of Subset of Closed Set of Metric Space is Subset
- Coefficients of Product of Two Polynomials
- Columns of Pascal's Triangle contain Simplicial Polytopic Numbers
- Definition:Commutative B-Algebra
- Compact Complement Topology is Second-Countable
- Compact Idempotent is of Finite Rank
- Compact Linear Transformation is Bounded
- Compact Linear Transformations Composed with Bounded Linear Operator
- Compact Operator on Hilbert Space Direct Sum
- Compact Self-Adjoint Operator has Countable Point Spectrum
- Compact Set of Irrational Numbers is Nowhere Dense
- Compact Set of Rational Numbers is Nowhere Dense
- Compact Subsets of T3 Spaces
- Compactness Properties in Hausdorff Spaces
- Complete Elliptic Integral of the First Kind as Power Series