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...

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...

and n are integers coprime with p. The modular inverse of n is an integer q such that n q = 1 + p h {\displaystyle nq=1+ph} for some integer h. Therefore...

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...

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...

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...

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

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 (...

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...

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...

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...

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...

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

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

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...

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...

{\displaystyle q_{i}} different from one are square-free integers that are pairwise coprime. This is called the square-free factorization of n. To construct...

an integer multiple of 2 π i . {\displaystyle 2\pi i.} If w = m n {\displaystyle w={\frac {m}{n}}} is a rational number with m and n coprime integers with...

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...

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

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...

b n a − b {\displaystyle {\frac {a^{n}-b^{n}}{a-b}}} with a, b any coprime integers, a > 1 and −a < b < a. (Since an − bn is always divisible by a − b...

{\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...

{p}{q}}\right|<{\frac {f(q)}{q}}} has infinitely many solutions in coprime integers p , q {\displaystyle p,q} with q > 0 {\displaystyle q>0} if and only...

{\displaystyle A^{x}+B^{y}=C^{z}} has no solutions in positive integers and pairwise coprime integers A, B, C if x, y, z ≥ 3. The conjecture was formulated in...

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...

{1}{q^{2+\varepsilon }}}} can have only finitely many solutions in coprime integers p {\displaystyle p} and q {\displaystyle q} . Roth's proof of this...

\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...