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**Mcbattle****Member**- Registered: 2014-01-29
- Posts: 5

So after I failed math last semester I got kicked into general math. But I already knew the concepts (I got a 94 after paying attention for less than 15 minutes over the course of 4 weeks) so I did what any other board 14 year does... screw around. I knew that if you take the remainder after dividing the Fibonacci numbers you see a pattern. However I noticed a pattern in the length of the patterns, but only when it was divided by certain numbers. The numbers in question would be 2^n for example:

2^1=2 The sequence is 3 numbers: 0,1,1

2^2=4 The sequence is 6 numbers: 0,1,1,2,3,1

2^3=8 The sequence is 12 numbers: 0,1,1,2,3,5,0,5,5,2,7,1

The pattern I noticed is that the length of the sequence is equal to

I have confirmed the same thing with 16 and 32 while in math by writing a program on my calculator. I was unable to go higher due to technical reasons though. I plan on looking into this later and seeing if it does continue.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,914

hi Mcbattle

Welcome to the forum.

Sorry, I'm not following you. Would you fill in more details for an old brain.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Mcbattle****Member**- Registered: 2014-01-29
- Posts: 5

Yes that is it. Or to make it easier it is the sum of the last two numbers in the sequence.

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I posted your query on another forum: http://www.artofproblemsolving.com/Foru … 8&t=573625.

As of now the thread has had 46 views but no reply.

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Ive been given this link (PDF):

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