What does this error mean? "error: incompatible types: possible lossy conversion from double to int" Am I doing something wrong with the syntax?

This is a java program to calculate Fermat's Last Theorem:
Fermat’s Last Theorem says that there are no integers a , b , and c such that

> aⁿ+bⁿ=cⁿ

except when n≤2 .

Write a program named Fermat.java that inputs four integers (a, b, c, and n) and checks to see if Fermat’s theorem holds.
If n is greater than 2 and   aⁿ+bⁿ=cⁿ  , the program should display

“Holy smokes, Fermat was wrong!”

Otherwise the program should display

“No, that doesn’t work.”

Tried making the parameters in checkFermat from int to double with no success.

This is my code:

import java.util.Scanner;

public class Fermat{
  public static void main(String[] args){
    Scanner scan = new Scanner(System.in);
    
    checkFermat(1,2,4,1);
  }

  public static void checkFermat(int a,int b,int c,int n){
    int result = ((Math.pow (a,n))+(Math.pow(b,n)));
    if ((((Math.pow(a, n)) + (Math.pow(b, n))) == (Math.pow(c, n))) && ((n != 2))) {
	  System.out.println("Holy smokes, Fermat was wrong!");
      
    }else{
      System.out.println("No, that doesn't work.");
    }
  }
}

Here is the error:

code/Fermat.java:11: error: incompatible types: possible lossy conversion from double to int
    int result = ((Math.pow (a,n))+(Math.pow(b,n)));
                                  ^
1 error

The method you use lies within java.lang.Math which goes as public static double pow(double, double). It expects both the base and exponent to be of the type double. Which works fine in this case (of passing integers) due to implicit type converging form int → double, as double has higher hierarchy, more number of bytes, greater precision and hence can store larger range of numbers.

Things become quite tricky when you reverse the operation. Which in this can can be noticed.

code/Fermat.java:11: error: incompatible types: possible lossy conversion from double to int
    int result = ((Math.pow (a,n))+(Math.pow(b,n)));
                                  ^
1 error

Here, the type needs to be converted from double → int as the return type of Math.pow(double, double) is of type double. The type should be either double or any other data type which will be more in hierarchy position than double. Which is not, the storing value is int which is way less than double and can cause loss of data, in terms of accuracy. Maybe returning value is a floating value which is not possible when it comes to integer numbers but range issue, some squaring of numbers may take a very large value incapable of storing within int, hence the error message you see is to inform you that the types is inappropriate and might be a cause for loss in precision.

How to overcome this ? <br>
1. Either use an appropriate data type <br>
(Recommended) Use the data type as expected for holding the returned data.<br>
For example: double result = ((Math.pow (a,n))+(Math.pow(b,n)));

2. Explicit type casting <br>
Explicitly say the compiler to cast down the data from double → int caring less about the data. <br>
For example: int result = (int)((Math.pow (a,n))+(Math.pow(b,n)));