Java.math.BigInteger.modInverse()方法在Java中的应用

前提是： 大整数基础知识

modPow()方法返回this的模块化乘法逆，mod m。如果m<=0或者this没有mod m的乘法逆（即gcd(this, m) !=1），该方法会抛出一个ArithmeticException。

语法

public BigInteger modInverse(BigInteger m)

参数： m – 模数。

返回值： 该方法返回一个BigInteger对象，其值为（（this）^（-1）mod m）。

异常

以下程序说明了BigInteger.modInverse()方法。

程序1 :

import java.math.*;import java.util.Scanner;  public class GFG {      public static void main(String[] args)    {          Scanner sc = new Scanner(System.in);          // create 2 BigInteger objects        BigInteger biginteger1, biginteger2, result;          // Initialize all BigInteger Objects        biginteger1 = new BigInteger("8");        biginteger2 = new BigInteger("21");          // perform modInverse operation on biginteger1 using biginteger2.        result = biginteger1.modInverse(biginteger2);          String expression = biginteger1 + " ^ -1 % "                            + biginteger2 + " = " + result;          // print result value        System.out.println(expression);    }}

输出:

8 ^ -1 % 21 = 8

程序2 :

import java.math.*;import java.util.Scanner;  public class GFG {      public static void main(String[] args)    {          Scanner sc = new Scanner(System.in);          // create 2 BigInteger objects        BigInteger biginteger1, biginteger2, result;          // Initialize all BigInteger Objects        biginteger1 = new BigInteger(88882);        biginteger2 = new BigInteger(22224);          // perform modInverse operation on biginteger1 using biginteger2.        result = biginteger1.modInverse(biginteger2);          String expression = biginteger1 + " ^ -1 % "                            + biginteger2 + " = " + result;          // print result value        System.out.println(expression);    }}

输出:

Exception in thread "main" java.lang.ArithmeticException: BigInteger not invertible.    at java.math.MutableBigInteger.modInverse(Unknown Source)    at java.math.MutableBigInteger.mutableModInverse(Unknown Source)    at java.math.BigInteger.modInverse(Unknown Source)    at BigInteger.GFG2.main(GFG2.java:23)

**参考: ** https://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html#modInverse(java.math.BigInteger).