Java.math.BigInteger.modInverse() method in Java

Prerequisite : BigInteger Basics The modInverse() method returns modular multiplicative inverse of this, mod m. This method throws an ArithmeticException if m <= 0 or this has no multiplicative inverse mod m (i.e., gcd(this, m) != 1). 

Syntax:

public BigInteger modInverse(BigInteger m)

Parameters: m – the modulus. 

Return Value: This method returns a BigInteger object whose value is ((this)^(-1) mod m). 

Exception:

• ArithmeticException – m <= 0, or this BigInteger has no multiplicative inverse mod m (that is, this BigInteger is not relatively prime to m).

Below programs illustrate the BigInteger.modInverse() method: 

Program 1 : 

Java

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);
    }
}

Output:

8 ^ -1 % 21 = 8

Program 2 : 

Java

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);
    }
}

Output :

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)

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