using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Codes_Maker
{
    public class FiniteFieldsMath
    {
        /// <summary>Сложение по модулю p.
        /// </summary>
        public static int Addition(int p, int x, int y)
        {
            return (x + y) % p;
        }
        /// <summary>Умножение по модулю p.
        /// </summary>
        public static  int Multiplication(int p, int x, int y)
        {
            int result = 0;
            result = (x * y) % p;
            if (result < 0) result = result + p;
            return result;
        }
        /// <summary>Вычитание по модулю p.
        /// </summary>
        public static int Subtraction(int p, int x, int y)
        {
            int result = 0;
            result = (x - y) % p;
            if (result < 0) result = result + p;
            return result;
        }
        /// <summary>Деление по модулю p.
        /// </summary>
        public static int Division(int p, int x, int y)
        {
            return Multiplication(p, x, Inversion(p, y));
        }
        /// <summary>Нахождение обратного элемента по модулю p.
        /// </summary>
        public static int Inversion(int p, int x)
        {
            int temp = 0, result = 0;
            for (int i = 1; i < p - 1; i++)
            {
                temp = Multiplication(p, x, i);
                if (temp == 1) result = i;
            }
            return result;
        }
    }
}