The Fibonacci sequence is defined by...

The Fibonacci sequence is defined by...

Postby Mellie » Fri Jul 24, 2015 11:50 am

The Fibonacci sequence is defined by [tex]F_1 = F_2 = 1[/tex] and [tex]F_{n + 2} = F_{n + 1} + F_n[/tex]. Find the remainder when [tex]F_{1999}[/tex] is divided by 5.





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Re: The Fibonacci sequence is defined by...

Postby Guest » Mon Aug 31, 2015 2:52 pm

The period of divizion by 5 is 16 - (1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,2,2,4,1,0).

[tex]1999 \equiv 15 \pmod{16}\Rightarrow F_{1999}\equiv 1 \pmod5[/tex]

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Re: The Fibonacci sequence is defined by...

Postby Guest » Fri May 12, 2017 10:47 pm

"The period of divizion by 5 is 16 - (1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,2,2,4,1,0).

There are 20 numbers in that sequence. so 1999[tex]\equiv[/tex]19 (mod 20). The 19th number is 1.

Right answer, wrong logic.

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