[section:extended_euclidean Extended Euclidean Algorithm]

[section Introduction]

The extended Euclidean algorithm solves the integer relation /mx + ny/ = gcd(/m/, /n/) for /x/ and /y/.

[endsect]

[section Synopsis]

    #include <boost/integer/extended_euclidean.hpp>

    namespace boost { namespace integer {

        template<class Z>
        std::tuple<Z, Z, Z> extended_euclidean(Z m, Z n);

    }}

[endsect]

[section Usage]

The tuple returned by the extended Euclidean algorithm contains, the greatest common divisor, /x/, and /y/, in that order:

    int m = 12;
    int n = 15;
    auto tup = extended_euclidean(m, n);

    int gcd = std::get<0>(tup);
    int x = std::get<1>(tup);
    int y = std::get<2>(tup);
    // mx + ny = gcd(m,n)

[endsect]

[section References]
Wagstaff, Samuel S., ['The Joy of Factoring], Vol. 68. American Mathematical Soc., 2013.

[endsect]
[endsect]
[/
Copyright 2018 Nick Thompson.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]