## Conjecture on the Fibonacci Numbers with an Index Equal to 2p Where P is Prime

**Authors:** Marius Coman

In this paper I make the following conjecture: If F(2*p) is a Fibonacci number with an index equal to 2*p, where p is prime, p ≥ 5, then there exist a prime or a product of primes q1 and a prime or a product of primes q2 such that F(2*p) = q1*q2 having the property that q2 – 2*q1 is also a Fibonacci number with an index equal to 2^n*r, where r is prime or the unit and n natural. Also I observe that the ratio q2/q1 seems to be a constant k with values between 2.2 and 2.237; in fact, for p ≥ 17, the value of k seems to be 2.236067(...).

**Comments:** 3 Pages.

**Download:** **PDF**

### Submission history

[v1] 2017-02-13 16:00:14

**Unique-IP document downloads:** 12 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*