"A Power Function"

Given the following function and it's results:

f(x,y) = x^y + y^x where x>0 and y>1

Using the above function denoted by f(x,y), and given that the initial values of x = 1 and y = 2, which increase by 1 each time, what are the last 4 digits of the sum of the first 15 function calls.

Note that ^ means exponent and that you are seeing the first 3 calls above.

Once you know the formula and math it's fairly simple, create a loop which runs the formula. add the result to the previous result to get the awnser.

The tricky bit os once you get into big numbers, with this code you should have "BC Math" enabled.

Awnser:

Source:

function solution(){
   $result = 0;
   for($i = 1; $i <= 15; $i++){
      $awns = bcadd( bcpow($i, ($i+1)) , bcpow(($i+1), $i)); 
	  $result = bcadd($result, $awns);
      echo "f(".$i.",".($i+1).") = ".$i."^".($i+1)." + ".($i+1)."^".$i." = ".number_format($awns)."<br />";
   }
   echo "Sum of these = ".number_format($result)."<br />";
}