Clust/Basic number theory

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Title: Basic number theory

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Basic number theory includes properties of natural numbers, integers, and rational numbers, including the Euclidean algorithm, primality, divisibility and factorization, linear Diophantine equations, and canonical decompositions.

Page name	Title
Def/Canonical decomposition into primes	Canonical decomposition into primes
Def/Composite number	Composite number
Def/Divides	Divides
Def/Division with remainder	Division of integers with remainder
Def/Euclidean algorithm	Euclidean algorithm
Def/Even	Even
Def/Greatest common divisor	Greatest common divisor
Def/Integer	Integer
Def/Least common multiple	Least common multiple
Def/Odd	Odd
Def/Prime number	Prime Number
Def/Relatively prime	Relatively prime
Def/Sequence of primes	Sequence of primes

Clust/Basic number theory

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Page name	Title
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
State/Canonical decompositions can be used to find GCD and LCM	Canonical decompositions can be used to find GCD and LCM.
State/Canonical decompositions of binomial coefficients	Canonical decompositions of binomial coefficients
State/Canonical decompositions of factorials	Canonical decompositions of factorials
State/Counting multiples of d between 1 and n	Counting multiples of d between 1 and n
State/Divisibility corresponds to inequalities of prime exponents	Divisibility corresponds to inequalities of prime exponents
State/Greatest common divisors can be computed pairwise	Greatest common divisors can be computed pairwise
State/Greatest common divisors can be found with the Euclidean algorithm	Greatest common divisors can be found with the Euclidean algorithm
State/Integers are relatively prime iff they have no common prime factors	Integers are relatively prime iff they have no common prime factors
State/Linear Diophantine equations can be solved with the Euclidean algorithm	Linear Diophantine equations can be solved with the Euclidean algorithm
State/Mutual divisibility of natural numbers implies equality	Mutual divisibility of natural numbers implies equality
State/Natural numbers are prime or composite or zero or one	Natural numbers are prime or composite or zero or one
State/Natural numbers can be factored into primes	Natural numbers can be factored into primes
State/Nonmultiples of a prime are relatively prime to the prime	Nonmultiples of a prime are relatively prime to the prime
State/Primes dividing a product must divide a factor	Primes dividing a product must divide a factor
State/Rational roots of integers are integers	Rational roots of integers are integers
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
State/The GCD times the LCM is the product	The GCD times the LCM is the product
State/The floor sum identity	The floor sum identity
State/There are infinitely many prime numbers	There are infinitely many prime numbers
State/Two out of three principle for divisibility	Two out of three principle for divisibility.
State/Uniqueness of prime factorization	Uniqueness of prime factorization