Is 707 a Fibonacci number

Answer 1

A Fibonacci number, is a number in the famous Fibonacci series, which is every new number after the two seed numbers (0, 1) are the sum of the previous two numbers:

0, 1, (0+1), (0+1+1), (0+1+1+1), (0+1+1+1+1+1), ...

0, 1, 1, 2, 3, 5, ...

Recursively, it can be written as:
Fn = Fn-1 + Fn-2

In order to use therecursiveformula, you would have to know the previous two terms. Without getting into too much detail, a simple formula you can use to see if a number is a fibonacci number, is to verify if (5N2 + 4) or (5N2 - 4) are perfect squares, where N is the number you are checking.

(5 (707)2 + 4 ) = 2,499,249

(5 (707)2- 4 ) = 2,499,241

√

2,499,249 ~= 1580.9 (not an integer)

√

2,499,241 ~= 1580.9 (also not an integer)

Therefore 707 is not a Fibonacci number.

To demonstrate how this works with a Fibonacci number, let's try 144.

(5 (144)2+ 4 ) = 103,684

(5 (144)2- 4 ) = 103,676

√

103,684 = 322 (is an integer => a perfect square)
√

103,676 ~= 321.988 (not an integer)

Only one of the tests has to be true, and therefore 144 is a Fibonacci number.