# Fermat’s Last Theorem

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 ` `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. `

## PHP

 ` `

Output:

```No counter example within given range and data
```

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