# The Fibonacci sequence is defined by...

### The Fibonacci sequence is defined by...

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

Mellie

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### Re: The Fibonacci sequence is defined by...

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).

$1999 \equiv 15 \pmod{16}\Rightarrow F_{1999}\equiv 1 \pmod5$

Guest

### Re: The Fibonacci sequence is defined by...

"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$\equiv$19 (mod 20). The 19th number is 1.

Guest

### Re: The Fibonacci sequence is defined by...

nice post

yasir7718

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