Definition:Primitive Prime Factor of Fibonacci Number

Definition

Let $F_n$ denote the $n$th Fibonacci number.

A primitive prime factor of $F_n$ is a prime number $p$ of $F_n$ such that:

$p \divides F_n$

$\nexists k \in \Z_{>0}: k < n: p \divides F_k$

where $a \divides b$ denotes that $a$ is a divisor of $b$.

That is, a prime factor of $F_n$ but of no smaller Fibonacci numbers.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $144$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $144$