/**
 * Extended Euclidean algorithm for solving the smallest
 * integer solution (|x| + |y| smallest) of the equation `Ax + By = gcd(x,y)`.
 *
 * @param a
 * @param b
 * @returns
 * @see https://me.guanghechen.com/post/math/number-theory/%E6%A8%A1%E6%96%B9%E7%A8%8B/basic/
 */
declare function euclidean(a: number, b: number): [number, number, number];
/**
 * Bigint version.
 *
 * @param a
 * @param b
 * @returns
 * @see https://me.guanghechen.com/post/math/number-theory/%E6%A8%A1%E6%96%B9%E7%A8%8B/basic/
 */
declare function euclideanBigint(a: bigint, b: bigint): [bigint, bigint, bigint];

/**
 * Find the greatest common divisor of x and y
 *
 * @param x
 * @param y
 * @returns
 */
declare function gcd(x: number, y: number): number;
/**
 * Bigint version.
 *
 * @param x
 * @param y
 * @returns
 */
declare function gcdBigint(x: bigint, y: bigint): bigint;

export { euclidean, euclideanBigint, gcd, gcdBigint };