Fibonacci Sum

Zeckendorf's Theorem states that every positive integer can be written uniquely as a sum of distinct non-neighboring Fibonacci number.

Find the sum of indices (0-indexing) such that their responding Fibonacci terms sums up to 99887766554433221100.

Clarification:

  • \(F_0 = 1, F_1 = 1\) and so on.
  • For 10, the answer is \(F_5 + F_2 = 8 + 2 = 10\). Sum of indices is \(5+2=7\).
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