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The following table lists all of the statements in the wiki.

Page Link	Title	Statement Type	Clusters
State/A OR B is logically equivalent to NOT A IMPLIES B	A OR B is logically equivalent to NOT A IMPLIES B	Fact	Clust/Logic and foundations
State/Additivity of polynomial degrees	Additivity of polynomial degrees	Proposition	Clust/The algebra of polynomials
State/Fields are integral domains	All fields are integral domains	Proposition	Clust/Basic ring theory
State/Arithmetic of residues is well-defined	Arithmetic of residues is well-defined	Proposition	Clust/Modular arithmetic
State/Arithmetic progression rule for binary quadratic forms	Arithmetic progression rule for binary quadratic forms	Proposition	Clust/Binary quadratic forms
State/Axiom of choice	Axiom of Choice	Axiom	Clust/ZFC axioms of set theory
State/Axiom of extensionality	Axiom of Extensionality	Axiom	Clust/ZFC axioms of set theory
State/Axiom of infinity	Axiom of Infinity	Axiom	Clust/ZFC axioms of set theory
State/Axiom of pairing	Axiom of Pairing	Axiom	Clust/ZFC axioms of set theory
State/Axiom of power sets	Axiom of Power Sets.	Axiom	Clust/ZFC axioms of set theory
State/Axiom of regularity	Axiom of Regularity	Axiom	Clust/ZFC axioms of set theory
State/Axiom of replacement	Axiom of Replacement	Axiom	Clust/ZFC axioms of set theory
State/Axiom of selection	Axiom of Selection	Axiom	Clust/ZFC axioms of set theory
State/Axiom of unions	Axiom of Unions	Axiom	Clust/ZFC axioms of set theory
State/Axiom of the empty set	Axiom of the empty set.	Axiom	Clust/ZFC axioms of set theory
State/Being relatively prime to a product is equivalent to being relatively prime to the factors	Being relatively prime to a product is equivalent to being relatively prime to the factors	Proposition	Clust/Basic number theory
State/Bijections are injective and surjective functions	Bijections are injective and surjective functions	Proposition	Clust/Functions
State/Binary quadratic forms are uniquely determined by their values at a superbasis	Binary quadratic forms are uniquely determined by their values at a superbasis	Proposition	Clust/Binary quadratic forms
State/Bounding riverbends of a given discriminant	Bounding riverbends of a given discriminant	Proposition
State/Bounding wells of a given discriminant	Bounding wells of a given discriminant	Proposition	Clust/Binary quadratic forms
State/Cancellation in groups	Cancellation in groups	Proposition	Clust/Basic group theory
State/Canonical decompositions can be used to find GCD and LCM	Canonical decompositions can be used to find GCD and LCM.	Proposition	Clust/Basic number theory
State/Canonical decompositions of binomial coefficients	Canonical decompositions of binomial coefficients	Proposition	Clust/Basic number theory
State/Canonical decompositions of factorials	Canonical decompositions of factorials	Proposition	Clust/Basic number theory
State/Centers of p-groups are nontrivial	Centers of p-groups are nontrivial	Proposition	Clust/Structure theory of finite groups
State/Chebyshev estimates for the prime number function	Chebyshev estimates for the prime number function	Theorem	Clust/Analytic number theory
State/Chinese remainder theorem	Chinese remainder theorem	Theorem	Clust/Modular arithmetic
State/Classification of subgroups of the integers	Classification of subgroups of $\ZZ$	Proposition	Clust/Basic group theory
State/Climbing in topographs	Climbing in topographs	Proposition	Clust/Binary quadratic forms
State/Composing injective surjective or bijective functions yields the same	Composing injective surjective or bijective functions yields the same	Proposition	Clust/Functions
State/Computing the totient of a prime power	Computing the totient of a prime power	Proposition	Clust/Modular arithmetic
State/Conjugacy of Sylow subgroups	Conjugacy of Sylow subgroups	Theorem	Clust/Structure theory of finite groups
State/Counting Sylow subgroups	Counting Sylow subgroups	Theorem	Clust/Structure theory of finite groups
State/Counting multiples of d between 1 and n	Counting multiples of d between 1 and n	Proposition	Clust/Basic number theory Clust/Basic counting
State/Counting subsets of a given cardinality	Counting subsets of a given cardinality	Proposition	Clust/Basic counting
State/Cyclic groups are classified by their order.	Cyclic groups are classified by their order.	Proposition	Clust/Basic group theory
State/Divisibility corresponds to containment of principal ideals	Divisibility corresponds to containment of principal ideals	Proposition	Clust/Basic ring theory
State/Divisibility corresponds to inequalities of prime exponents	Divisibility corresponds to inequalities of prime exponents	Proposition	Clust/Basic number theory
State/Estimate for the product of primes	Estimate for the product of primes	Proposition
State/Eulers criterion	Euler Criterion	Proposition	Clust/Theory of quadratic residues
State/Every arc of river is finite	Every arc of river is finite	Proposition	Clust/Binary quadratic forms
State/Every lax vector in a lax basis is primitive	Every lax vector in a lax basis is primitive	Proposition	Clust/Binary quadratic forms
State/Every nonempty subset of N has a smallest element	Every nonempty subset of N has a smallest element.	Proposition	Clust/Properties of natural numbers
State/Every primitive lax vector belongs to a lax basis	Every primitive lax vector belongs to a lax basis	Proposition	Clust/Binary quadratic forms
State/Existence of Sylow subgroups	Existence of Sylow subgroups	Theorem	Clust/Structure theory of finite groups
State/Existence of wells for definite forms	Existence of wells for definite forms	Proposition	Clust/Binary quadratic forms
State/Fermats little theorem	Fermat's little theorem	Theorem	Clust/Modular arithmetic
State/Fermat Euler theorem	Fermat-Euler theorem	Theorem	Clust/Modular arithmetic
State/Finite sets can be counted	Finite sets can be counted	Proposition	Clust/Naive set theory
State/First isomorphism theorem for groups	First isomorphism theorem for groups	Proposition	Clust/Basic group theory
State/Fundamental theorem of algebra	Fundamental theorem of algebra	Theorem	Clust/Complex analysis Clust/Field theory
State/Greatest common divisors can be computed pairwise	Greatest common divisors can be computed pairwise	Proposition	Clust/Basic number theory
State/Greatest common divisors can be found with the Euclidean algorithm	Greatest common divisors can be found with the Euclidean algorithm	Proposition	Clust/Basic number theory
State/Groups of prime order are cyclic	Groups of prime order are cyclic	Proposition	Clust/Structure theory of finite groups
State/Groups of prime squared order are abelian	Groups of prime squared order are abelian	Proposition	Clust/Structure theory of finite groups
State/Half of nonzero residues are quadratic residues	Half of nonzero residues are quadratic residues	Proposition	Clust/Theory of quadratic residues
State/Homomorphic images of subgroups are subgroups	Homomorphic images of subgroups are subgroups	Proposition
State/Induction	Induction	Theorem	Clust/Properties of natural numbers
State/Inequality in N corresponds to existence of differences	Inequality in N corresponds to existence of differences	Proposition	Clust/Properties of natural numbers
State/Injective functions have left inverses	Injective functions have left inverses	Proposition	Clust/Functions
State/Integers are relatively prime iff they have no common prime factors	Integers are relatively prime iff they have no common prime factors	Proposition	Clust/Basic number theory
State/Intersections of subspaces are subspaces	Intersections of subspaces are subspaces	Proposition	Clust/Linear algebra
State/Inversion is an antiautomorphism	Inversion is an antiautomorphism	Proposition	Clust/Basic group theory
State/Irreducible implies prime in a PID	Irreducible elements of a PID are prime.	Proposition	Clust/Factorization in rings
State/Kernel criterion for injectivity of group homomorphisms	Kernel criterion for injectivity of group homomorphisms	Proposition	Clust/Basic group theory
State/Lagranges theorem	Lagrange's Theorem	Theorem	Clust/Basic group theory
State/Linear Diophantine equations can be solved with the Euclidean algorithm	Linear Diophantine equations can be solved with the Euclidean algorithm	Proposition	Clust/Basic number theory
State/Minmax addition formula	Minmax addition formula	Proposition	Clust/Properties of natural numbers
State/Multiplication increases size	Multiplication increases size.	Fact	Clust/Arithmetic in N
State/Multiplicative inverses exist mod p	Multiplicative inverses exist mod p	Proposition	Clust/Modular arithmetic
State/Multiplicativity of the totient	Multiplicativity of the totient	Proposition	Clust/Modular arithmetic
State/Mutual divisibility of natural numbers implies equality	Mutual divisibility of natural numbers implies equality	Proposition	Clust/Basic number theory
State/N is totally ordered	N is totally ordered	Proposition	Clust/Properties of natural numbers
State/Natural numbers are prime or composite or zero or one	Natural numbers are prime or composite or zero or one	Proposition	Clust/Basic number theory
State/Natural numbers can be factored into primes	Natural numbers can be factored into primes	Proposition	Clust/Basic number theory
State/No set is an element of itself	No set is an element of itself	Proposition	Clust/Basic set theory
State/Nonmultiples of a prime are relatively prime to the prime	Nonmultiples of a prime are relatively prime to the prime	Proposition	Clust/Basic number theory
State/Nonzero naturals are successors	Nonzero naturals are successors	Fact	Clust/Properties of natural numbers
State/Nilpotents are zero divisors	Nonzero nilpotents are zero divisors	Proposition	Clust/Basic ring theory
State/Periodicity along the river	Periodicity along the river	Proposition	Clust/Binary quadratic forms
State/Permutations can be decomposed into transpositions	Permutations can be decomposed into transpositions	Proposition	Clust/Permutations
State/Primes dividing a product must divide a factor	Primes dividing a product must divide a factor	Proposition	Clust/Basic number theory
State/Product of units is a unit	Product of units is a unit	Proposition	Clust/Basic ring theory
State/Products of invertible residues are invertible	Products of invertible residues are invertible	Proposition	Clust/Modular arithmetic
State/Quadratic reciprocity	Quadratic Reciprocity	Theorem	Clust/Theory of quadratic residues
State/Rational roots of integers are integers	Rational roots of integers are integers	Theorem	Clust/Basic number theory
State/Relative primality to the modulus is equivalent to invertibility of a residue	Relative primality to the modulus is equivalent to invertibility of a residue	Proposition	Clust/Modular arithmetic
State/Root counting over a field	Root counting over a field	Proposition	Clust/The algebra of polynomials
State/Solutions to homogeneous linear Diophantine equations can be found with the LCM	Solutions to homogeneous linear Diophantine equations can be found with the LCM	Proposition	Clust/Basic number theory
State/Solving quadratic Diophantine equations in two variables	Solving quadratic Diophantine equations in two variables	Proposition	Clust/Binary quadratic forms
State/Squares are nonnegative in an ordered field	Squares are nonnegative in an ordered field	Proposition	Clust/Ordered ring theory
State/Surjective functions have right inverses	Surjective functions have right inverses	Proposition	Clust/Functions
State/Systems of two linear Diophantine equations	Systems of two linear Diophantine equations	Proposition	Clust/Binary quadratic forms
State/The GCD times the LCM is the product	The GCD times the LCM is the product	Proposition	Clust/Basic number theory
State/The domain topograph has no circuits	The domain topograph has no circuits	Proposition	Clust/Binary quadratic forms
State/The empty set is a subset of every set	The empty set is a subset of every set.	Proposition
State/The floor sum identity	The floor sum identity	Proposition	Clust/Basic number theory Clust/Basic counting
State/Intersections of ideals are ideals	The intersection of ideals is an ideal	Proposition	Clust/Basic ring theory
State/Intersections of subgroups are subgroups	The intersection of subgroups is a subgroup.	Proposition	Clust/Basic group theory
State/There are infinitely many prime numbers	There are infinitely many prime numbers	Theorem	Clust/Basic number theory
State/No nonzero nilpotents in a field	There are no nonzero nilpotents in a field.	Proposition	Clust/Basic ring theory
State/There are no zero divisors mod p	There are no zero divisors mod p	Proposition	Clust/Modular arithmetic
State/Triangle inequalities	Triangle inequalities	Proposition	Clust/Coordinate plane geometry
State/Truth by false premise	Truth by False Premise	Fact	Clust/Logic and foundations
State/Two out of three principle for divisibility	Two out of three principle for divisibility.	Proposition	Clust/Basic number theory Clust/Basic ring theory
State/Uniqueness of identity element in a monoid	Uniqueness of identity element in a monoid or group	Fact	Clust/Basic group theory
State/Uniqueness of prime factorization	Uniqueness of prime factorization	Theorem	Clust/Basic number theory
State/Uniqueness of inverse elements in a monoid	Uniqueness_of_inverse_elements_in_a_monoid	Fact	Clust/Basic group theory
State/Values in the range topograph adjacent to a given face form a quadratic sequence	Values in the range topograph adjacent to a given face form a quadratic sequence	Proposition	Clust/Binary quadratic forms
State/Zolotarevs lemma	Zolotarev's Lemma	Lemma	Clust/Theory of quadratic residues