Java(Algebra: perfect square) Write a program that prompts the user to enter an integer m and find the smallest integer n such that m * n is a perfect square. (Hint: Store all smallest factors of m into an array list. n is the product of the factors that appear an odd number of times in the array list. For example, consider m = 90, store the factors 2, 3, 3, and 5 in an array list. 2 and 5 appear an odd number of times in the array list. Thus, n is 10.) Here are some sample runs: Enter an integer m: 1500 The smallest number n for m * n to be a perfect square is 15 m * n is 22500

Here's the Java code to solve this problem:

import java.util.*;

public class PerfectSquare {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        System.out.print("Enter an integer m: ");
        int m = input.nextInt();
        List<Integer> factors = getSmallestFactors(m);
        int n = 1;
        for (int factor : factors) {
            if (getFrequency(factors, factor) % 2 != 0) {
                n *= factor;
            }
        }
        System.out.println("The smallest number n for m * n to be a perfect square is " + n);
        System.out.println("m * n is " + (m * n * n));
    }
    
    public static List<Integer> getSmallestFactors(int n) {
        List<Integer> factors = new ArrayList<>();
        int factor = 2;
        while (n > 1) {
            if (n % factor == 0) {
                factors.add(factor);
                n /= factor;
            } else {
                factor++;
            }
        }
        return factors;
    }
    
    public static int getFrequency(List<Integer> list, int value) {
        int count = 0;
        for (int element : list) {
            if (element == value) {
                count++;
            }
        }
        return count;
    }
    
}

Explanation:

The `getSmallestFactors` method takes an integer `n` as input and returns a list of its smallest factors. It does this by repeatedly dividing `n` by its smallest factor until `n` becomes 1.

The `getFrequency` method takes a list of integers and a value as input and returns the number of times the value appears in the list.

In the `main` method, we first prompt the user to enter an integer `m`. Then we call `getSmallestFactors` to get the list of smallest factors of `m`. We then iterate through the list of factors and multiply the ones that appear an odd number of times. This gives us the smallest integer `n` such that `m * n` is a perfect square. Finally, we print out the value of `n` and `m * n * n`.