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numtheory(deprecated)

 migcdex
 compute solutions to the modulo N extended GCD problem

 Calling Sequence migcdex(N, a, b1, b2, ..., bn)

Parameters

 N - positive integer a - integer b1, b2, ..., bn - integers

Description

 • Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[ModExtendedGCD] instead.
 • The function migcdex computes a solution to the modulo $N$ greatest common divisor problem for an arbitrary number of integers.
 • The return value is the sequence $\mathrm{c1},\mathrm{c2},...,\mathrm{cn}$ of non-negative integers with

$\mathrm{gcd}\left(N,a,{b}_{1},...,{b}_{n}\right)=\mathrm{gcd}\left(N,\left(a+{c}_{1}{b}_{1}+...+{c}_{n}{b}_{n}\right)\right)$

 such that $\left({c}_{n},...,{c}_{2},{c}_{1}\right)$ is lexicographically minimal among all such sequences.

Examples

Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[ModExtendedGCD] instead.

 > $\mathrm{with}\left(\mathrm{numtheory}\right):$
 > $\mathrm{migcdex}\left(150,0\right)$
 > $\mathrm{migcdex}\left(150,5,75,25\right)$
 ${0}{,}{0}$ (1)
 > $\mathrm{migcdex}\left(150,9,75,25\right)$
 ${1}{,}{1}$ (2)

 See Also