Fibonomial Coefficient is Integer

Theorem
Let $\dbinom n k_\mathcal F$ be a Fibonomial coefficient.

Then $\dbinom n k_\mathcal F$ is an integer.

Proof
Recurrence Relation for Fibonomial Coefficients gives:


 * $\dbinom n k_\mathcal F = F_{k - 1} \dbinom {n - 1} k_\mathcal F + F_{n - k + 1} \dbinom {n - 1} {k - 1}_\mathcal F$

where $F_{k - 1}$ etc. denote Fibonacci numbers.

It follows that each Fibonomial coefficient is the sum of integers, and so an integer.