According to Fermat’s Last Theorem, no three positive integers a, b, c satisfy the equation, 
for any integer value of n greater than 2. For n = 1 and n = 2, the equation have infinitely many solutions.
Some solutions for n = 1 are, 2 + 3 = 5 7 + 13 = 20 5 + 6 = 11 10 + 9 = 19 Some solutions for n = 2 are,
C++
// C++ program to verify fermat's last theorem// for a given range and n.#include <bits/stdc++.h>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 codeint 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 codetestSomeNumbers(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. |
PHP
<?php// PHP program to verify fermat's// last theorem for a given range //and n.function testSomeNumbers($limit, $n){ if ($n < 3) for($a = 1; $a <= $limit; $a++) for($b = $a; $b <= $limit; $b++) { // 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); $c_pow = pow($c, $n); if ($c_pow != $pow_sum) { echo "Count example found"; return; } } echo "No counter example within ". "given range and data";} // Driver Code testSomeNumbers(10, 3);// This code is contributed by m_kit?> |
Javascript
<script>// 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); </script> |
Output:
No counter example within given range and data
Time Complexity: O(m2logn) , where m is the limit
Auxiliary Space: O(1)
Please suggest if someone has a better solution which is more efficient in terms of space and time.
This article is contributed by Aarti_Rathi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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