The complexity of greatest common divisor computations

We study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers. We prove the NP-completeness of finding an optimal set of multipliers with respect to either the L0 metric or the L norm. We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give an upper bound on the size of the largest multiplier produced by this method, which is optimal.

• Type: Conference
• Year: 1994
• Where: ANTS
• Authors: Bohdan S. Majewski, George Havas
• Keywords: Algorithms, ANTS 1994, Greatest Common Divisor, Linear Combination, Positive Numbers