费马最后定理

根据费马最后定理，没有三个正整数a，b，c满足该方程， $a^n + b^n = c^n$对于任何大于2的n整数。对于n = 1和n = 2，该方程式具有无限多个解。

n = 1的一些解为2 + 3 = 5 7 + 13 = 20 5 + 6 = 11 10 + 9 = 19 $5^2 + 12^2 = 13^2 3^2 + 4^2 = 5^2 8^2 + 15^2 = 17^2 9^2 + 40^2 = 41^2$

C++

// C++ program to verify fermat's last theorem
// for a given range and n.
#include 
using namespace std;
 
void testSomeNumbers(int limit, int n)
{
   if (n < 3)
     return;
 
   for (int a=1; a<=limit; a++)
     for (int b=a; b<=limit; b++)
     {
         // Check if there exists a triplet
         // such that a^n + b^n = c^n
         int pow_sum = pow(a, n) + pow(b, n);
         double c = pow(pow_sum, 1.0/n);
         int c_pow = pow((int)c, n);
         if (c_pow == pow_sum)
         {
             cout << "Count example found";
             return;
         }
     }
 
     cout << "No counter example within given"
            " range and data";
}
 
// driver code
int main()
{
    testSomeNumbers(10, 3);
    return 0;
}

Java

// Java program to verify fermat's last theorem
// for a given range and n.
import java.io.*;
 
class GFG
{
    static void testSomeNumbers(int limit, int n)
    {
        if (n < 3)
            return;
         
        for (int a = 1; a <= limit; a++)
            for (int b = a; b <= limit; b++)
            {
                // Check if there exists a triplet
                // such that a^n + b^n = c^n
                int pow_sum = (int)(Math.pow(a, n)
                               + Math.pow(b, n));
                double c = Math.pow(pow_sum, 1.0 / n);
                int c_pow = (int)Math.pow((int)c, n);
                if (c_pow == pow_sum)
                {
                    System.out.println("Count example found");
                    return;
                }
            }
         
            System.out.println("No counter example within given"+
                               " range and data");
    }
     
    // Driver code
    public static void main (String[] args)
    {
        testSomeNumbers(12, 5);
     
    }
}
 
// This code is contributed by vt_m.

Python3

# Python3 program to verify fermat's last
# theorem for a given range and n.
 
def testSomeNumbers(limit, n) :
 
    if (n < 3):
        return
     
    for a in range(1, limit + 1):
        for b in range(a, limit + 1):
         
            # Check if there exists a triplet
            # such that a^n + b^n = c^n
            pow_sum = pow(a, n) + pow(b, n)
            c = pow(pow_sum, 1.0 / n)
            c_pow = pow(int(c), n)
             
            if (c_pow == pow_sum):
                print("Count example found")
                return
    print("No counter example within given range and data")
 
# Driver code
testSomeNumbers(10, 3)
 
# This code is contributed by Smitha Dinesh Semwal.

C#

// C# program to verify fermat's last theorem
// for a given range and n.
using System;
 
class GFG {
     
    static void testSomeNumbers(int limit, int n)
    {
        if (n < 3)
            return;
         
        for (int a = 1; a <= limit; a++)
            for (int b = a; b <= limit; b++)
            {
                 
                // Check if there exists a triplet
                // such that a^n + b^n = c^n
                int pow_sum = (int)(Math.Pow(a, n)
                                + Math.Pow(b, n));
                double c = Math.Pow(pow_sum, 1.0 / n);
                int c_pow = (int)Math.Pow((int)c, n);
                 
                if (c_pow == pow_sum)
                {
                    Console.WriteLine("Count example found");
                    return;
                }
            }
         
            Console.WriteLine("No counter example within"
                                + " given range and data");
    }
     
    // Driver code
    public static void Main ()
    {
        testSomeNumbers(12, 3);
     
    }
}
 
// This code is contributed by vt_m.

Javascript

 
// JavaScript program to verify fermat's last theorem
// for a given range and n.
 
    function testSomeNumbers(limit, n)
    {
        if (n < 3)
            return;
           
        for (let a = 1; a <= limit; a++)
            for (let b = a; b <= limit; b++)
            {
                // Check if there exists a triplet
                // such that a^n + b^n = c^n
                let pow_sum = (Math.pow(a, n)
                               + Math.pow(b, n));
                let c = Math.pow(pow_sum, 1.0 / n);
                let c_pow = Math.pow(Math.round(c), n);
                if (c_pow == pow_sum)
                {
                    document.write("Count example found");
                    return;
                }
            }
           
            document.write("No counter example within given"+
                               " range and data");
    }
  
 
// Driver Code
 
        testSomeNumbers(12, 5);
           

输出：

No counter example within given range and data