gcdmn1

gcdmn1 is a term used in mathematical and computational literature to denote a generalized greatest common divisor operation over a sequence of integers. It is also used as the name of a lightweight conceptual software library designed to implement multi-argument gcd computations and related number-theoretic utilities. Because gcdmn1 is not tied to a single standard definition, entries in different contexts may emphasize different aspects, but all share the core idea of extending gcd beyond two numbers to many operands.

In mathematics, gcdmn1 typically refers to gcd(a1, a2, ..., an), which is the largest positive integer that divides every a_i. It is computed by iteratively applying the two-argument gcd, using the Euclidean algorithm. Properties include gcd(a1,0,...,0) = |a1|, gcd(0,...,0) = 0, and gcd is associative up to the order of operands.

The gcdmn1 software concept provides APIs for computing gcd across lists, streams, or big integers, with optimizations for large input sets and for languages with big-integer support. It may include utilities to normalize sign, handle negative inputs, and report common divisors for subsets or constrained gcd values.

In applications, gcdmn1 is relevant to factorization, modular arithmetic, cryptography, and algorithmic number theory. It is sometimes introduced in tutorials as a practical example of multi-argument gcd computation.

Because gcdmn1 is not a formal standard, discussions vary in exact definitions and features. See also gcd, lcm, extended Euclidean algorithm.