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Problem  6
A Power Function


Given the following function and it's results:

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

f(1,2) = 1^2 + 2^1 = 3
f(2,3) = 2^3 + 3^2 = 17
f(3,4) = 3^4 + 4^3 = 145
.
 .
  .

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.


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Date added
2008-09-06
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