According to Fermat’s Last Theorem, no three positive integers a, b, c satisfy the equation,
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 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
<?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.