greatest common divisor


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  • noun

Synonyms for greatest common divisor

the largest integer that divides without remainder into a set of integers

References in periodicals archive ?
Let [alpha] = [[[alpha].sub.1], [[alpha].sub.2], ..., [[alpha].sub.N+1]] be a list of integers with greatest common divisor equal to 1, and let
If B is a nonempty subset of a semimodule A over a semiring R, then an element b of A is a greatest common divisor of B if and only if the following conditions are satisfied:
This textbook for an undergraduate introductory course in number theory begins with the ancient Euclidean algorithm for finding the greatest common divisor of two integers, and ends with the theory of elliptic curves and some other modern developments.
The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties.
The assumption that the greatest common divisor of {k [member of] N | [a.sub.k] = [not equal to] 0} is 1 means that [theta] = 0.Therefore z = [r.sub.0], and we conclude that r0 is a unique zero of g(t) having the smallest absolute value of all zeros of g(t).
Let (a, b) = d denotes the Greatest Common Divisor of a and b, and a = d x [a.sub.1], b = d x [b.sub.1].
Since we will make connections between periodicity of trigonometric functions and the concepts of greatest common divisor and the least common multiple that are defined only for integers, we need to provide extended definition of the terms "divisor", "multiple", "greatest common divisor" and the "least common multiple" of rational numbers.
, [x.sub.t]] denote the greatest common divisor and the least common multiple of any positive integers [x.sub.1], [x.sub.2], ...
Assume that (u, v) is the greatest common divisor of u and v, then we have
To understand the statement of Dirichlet's theorem, recall that given two integers a and b, their greatest common divisor is the largest integer which is a divisor of both a and b; we denote it gcd(a,b).
where (s(n),m) denotes the greatest common divisor of s(n) and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [epsilon] is any positive number.