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If every pair in a set of integers is coprime, then the set is said to be pairwise coprime (or pairwise relatively prime, mutually coprime or mutually relatively prime). Pairwise coprimality is a stronger condition than setwise coprimality; every pairwise coprime finite set is also setwise coprime, but the reverse is not true. For example, the ...
Assume that is an odd prime, that + + = for pairwise relatively prime integers (i.e. in ) ,, and that . This is the first case of Fermat's Last Theorem. (The second case is when .
Pairwise generally means "occurring in pairs" or "two at a time." Pairwise may also refer to: Pairwise disjoint; Pairwise independence of random variables; Pairwise comparison, the process of comparing two entities to determine which is preferred; All-pairs testing, also known as pairwise testing, a software testing method.
The nonnegative integer is called the free rank or Betti number of the module . The module is determined up to isomorphism by specifying its free rank r , and for class of associated irreducible elements p and each positive integer k the number of times that p k occurs among the elementary divisors.
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
In mathematics, an element a of a commutative ring R is called (relatively) prime to an ideal I if whenever ab is an element of I then b is also an element of I. A proper ideal I of a commutative ring A is said to be primal if the elements that are not prime to it form an ideal.
But in such a large, complex market, items frequently fall through the cracks, so if you do discover a counterfeit item in your Amazon Prime box, Dimyan suggests two actions. "Utilize Amazon's ...
In number theory, Carmichael's theorem, named after the American mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind U n (P, Q) with relatively prime parameters P, Q and positive discriminant, an element U n with n ≠ 1, 2, 6 has at least one prime divisor that does not divide any earlier one except the 12th Fibonacci number F(12) = U 12 (1, − ...