i] have greatest common divisor 1, we have [zeta] = 1 as a pole of order N + 1, and the other poles have order strictly less.
N+1]] be a list of integers with greatest common divisor equal to 1, and let
Let n and k be positive integers, n > k, and let d be their greatest common divisor
Among the topics are multivariate ultrametric root counting, efficient polynomial system solving by numerical methods, a search for an optimal start system for numerical homotopy continuation, dense fewnomials, and the numerical greatest common divisor
of univariate polynomials.
Let (a, b) = d denotes the Greatest Common Divisor
of a and b, and a = d x [a.
t]] denote the greatest common divisor
and the least common multiple of any positive integers [x.
Assume that (u, v) is the greatest common divisor
of u and v, then we have
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.
The nonsingularity criterion is related to the greatest common divisors
of two polynomials, henceforth denoted by gcd(*, *).
Among the topics are greatest common divisors
, integer multiples and exponents, quotients of polynomial rings, divisibility and factorization in integral domains, subgroups of cyclic groups, cosets and Lagrange's theorem, the fundamental theorem of finite abelian groups, and check digits.
A professor from Pierre and Marie Curie University presents an algorithm for computing the radius of convergence function for first order differential equations, and a professor from the University of North Texas proves the existence of greatest common divisors
and factorization in rings of non-Archimedean entire functions.
This means that all numbers that are not multiples of 13 have no common divisors
with 13 except for the number one.