Fibonacci Divisibility

Problem #69

Tags: mathematics modulo puzzle

Who solved this?

You may refer to Fibonacci Sequence task if you are unfamiliar with the subject.

Given usual Fibonacci Sequence, starting with 0 and 1:

0 1 1 2 3 5 8 13 21 34 ...

and some value M you will be asked to find the index of the first non-zero member of this list, which is evenly divisible by this M, e.g. if you are given M = 17 the answer is 9 (the index of the element 34).

Input data in the first line will contain the number of test-cases.
Next line will contain exactly this of divisors M (not exceeding 10000) for which you should give answers.
Answer should contain indices of members of Fibonacci Sequence, separated by spaces.


input data:
17 12 61

9 12 15
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