In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them...

the integers coprime (relatively prime) to n from the set { 0 , 1 , … , n − 1 } {\displaystyle \{0,1,\dots ,n-1\}} of n non-negative integers form a...

An integer triangle or integral triangle is a triangle all of whose side lengths are integers. A rational triangle is one whose side lengths are rational...

{\displaystyle k} is a (possibly negative) integer, n {\displaystyle n} and d {\displaystyle d} are coprime integers both coprime with p {\displaystyle p} , and d...

fraction ⁠ a b , {\displaystyle {\tfrac {a}{b}},} ⁠ where a and b are coprime integers and b > 0. This is often called the canonical form of the rational...

n_{k}} be k pairwise coprime integers greater than one, a 1 , … , a k {\displaystyle a_{1},\dots ,a_{k}} be k arbitrary integers, and N be the product...

parameters m and n are positive coprime integers that are not both odd. By multiplying a, b and c by an arbitrary positive integer, one gets a parametrization...

c=k\cdot (m^{2}+n^{2})} where m, n, and k are positive integers with m > n, and with m and n coprime and not both odd. That these formulas generate Pythagorean...

as an ideal in the ring of integers, which is closely related to GCD. If gcd(a, b) = 1, then a and b are said to be coprime (or relatively prime). This...

whose leading coefficient is 1) whose coefficients are integers. The set of all algebraic integers A is closed under addition, subtraction and multiplication...

multiplicative group of the integers modulo m that are invertible. It consists of the congruence classes am, where a is coprime to m; these are precisely...

Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q are not coprime (in which case the number of components...

which the sum of two coprime integers, each a power of an integer, with the powers not necessarily equal, can equal another integer that is a power, with...

of values (am, bn, ck), where a, b, c are positive coprime integers and m, n, k are positive integers satisfying The statement is about the finiteness of...

\text{rad}}(2^{6}\cdot 5^{6})=2\cdot 5=10} If a, b, and c are coprime positive integers such that a + b = c, it turns out that "usually" c < rad ( a b...

any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer. In other words, there...

degree two with integer coefficients. Because of the homogeneity, one can consider only parameters that are setwise coprime integers. If Q ( X 0 , … ...

the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that a x + b y = gcd (...

of values (am, bn, ck) where a, b, c are positive coprime integers and m, n, k are positive integers satisfying The inequality on m, n, and k is a necessary...

Start with a 2 × 2 array and insert two coprime positive integers (q,q′) in the top row. Place the even integer (if any) in the left-hand column. [ q q...

algorithm is known that can factor integers in polynomial time. However, Shor's algorithm shows that factoring integers is efficient on an ideal quantum...

states that if x and y are coprime integers (i.e. they share no common divisors other than 1 and −1) there exist integers r and s such that r x + s y...

division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the...

{\displaystyle a+nd,\ } where n runs through the positive integers and a and d are any given positive coprime integers with 1 ≤ a ≤ d − 1, then: p ⁡ ( a , d ) < c d...

theorem or Euler's totient theorem) states that, if n and a are coprime positive integers, then a φ ( n ) {\displaystyle a^{\varphi (n)}} is congruent to...

decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater...

the primitive nth roots of unity are those for which k and n are coprime integers. Subsequent sections of this article will comply with complex roots...

(φ) function) in number theory, counting the number of coprime integers less than an integer. Euler hypergeometric integral Euler–Riemann zeta function...

number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and...

system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is...