×

# Fibonacci ??? Help me

Have anyone noticed that when we take 4 consecutive numbers in the Fibonacci list: f(x), f(x+1), f(x+2), f(x+3). We will have:

f(x) * f(x+3) - f(x+1) * f(x+2) =1 or -1

For example: 2 * 8 - 3 * 5 =1

p/s: It is just my view, I do not sure if it is always true.

Note by Khoi Nguyen Ho
3 years, 4 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

That is a great observation.

Let me suggest a way of continuing:
Can you list out the values of $$x$$ where the expression is 1, and the values of $$x$$ where the expression is -1?
Do you know Binet's formula which gives you the value of $$f(x)$$?

Staff - 3 years, 4 months ago

oh yeah, just adding x, x+1, x+2, x+3 into the Binet's and then minus two products, I found that f(x) * f(x+3) - f(x+1) * f(x+2)= -1 * (-1)^x. Great. Thank you.

- 3 years, 4 months ago

Hmm.........AM SPEECHLESS

- 3 years, 4 months ago