(Im)possible to construct

\[ \large a^3+b^5+c^7+d^9+e^{11}\]

For positive integers \(a,b,c,d\) and \(e\), determine the number of positive integers (greater than 1000) that cannot be represented by the expression above.

Details and Assumptions

  • If you think all numbers can be represented this way, enter your answer as 0.
  • If you think there are infinitely many numbers that cannot be represented this way, enter your answer as 9999999.
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