Fibonacci subs
Consider the Fibonacci numbers :
- F 0 = 0
- F 1 = 1
- F n = F n − 1 + F n − 2 for n > 1
For some integer m :
F F F F m = m
F F F F m + 1 = m + 1
m = ?
If you think there is no solution, provide − 1 as your answer.
If you think there are multiple solutions, provide − 2 as your answer.
The answer is -2.
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1 solution
Doesn't F n = n − 1 for 1 < n ≤ 3 ?
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Actually, for 1 < n ≤ 4
Oooops.... I goofed... You're right. You caught me in a lie. The answer should be -2, then, right? Since m could be 1 or 5? @Calvin Lin do you agree?
If we write down the sequence
| n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | … |
| F n | 0 | 1 | 1 | 2 | 3 | 5 | 8 | … |
we see that there are three fixed points – two with positive n –, n = 0 , 1 , 5 .
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Right you are! The answer needs to be updated to -2.
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You could also ask for the maximum possible value of m .
The answer should be changed to -2 since m can be 1 or 5. Sorry about that.