Java Program to Implement Fermat Factorization Algorithm

This is a Java Program to Implement Fermat Factorization Algorithm. Fermat’s factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: N = a² – b². That difference is algebraically factorable as (a + b)(a – b); if neither factor equals one, it is a proper factorization of N.

Here is the source code of the Java Program to Implement Fermat Factorization Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

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/**
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 ** Java Program to implement Fermat Factorization Algorithm

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 **/
```
```
 
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import java.util.Scanner;
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public class FermatFactorization
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```
{
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    /** Fermat factor **/
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    public void FermatFactor(long N)
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    {
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        long a = (long) Math.ceil(Math.sqrt(N));

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        long b2 = a * a - N;
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        while (!isSquare(b2))
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        {
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            a++;
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            b2 = a * a - N;
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        }
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        long r1 = a - (long)Math.sqrt(b2);

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        long r2 = N / r1;
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        display(r1, r2);
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    }
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    /** function to display roots **/
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    public void display(long r1, long r2)

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    {
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        System.out.println("\nRoots = "+ r1 +" , "+ r2);

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    }
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    /** function to check if N is a perfect square or not **/

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    public boolean isSquare(long N)
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    {
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        long sqr = (long) Math.sqrt(N);
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        if (sqr * sqr == N || (sqr + 1) * (sqr + 1) == N)

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            return true;
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        return false;
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    }
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    /** main method **/
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    public static void main(String[] args)

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    {
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        Scanner scan = new Scanner(System.in);

        System.out.println("Fermat Factorization Test\n");

        System.out.println("Enter odd number");

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        long N = scan.nextLong();
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        FermatFactorization ff = new FermatFactorization();

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        ff.FermatFactor(N);
```
```
    }
```
```
}
```

Fermat Factorization Test
 
Enter odd number
5959
 
Roots = 59 , 101
 
 
Fermat Factorization Test
 
Enter odd number
432633
 
Roots = 499 , 867

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