Arithmetic properties of q-Fibonacci numbers and q-Pell numbers

We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.Comment: 12 page

A note on the Polignac numbers

Suppose that $k\geq 3.5\times 10^6$ and \hH=\{h_1,\ldots,h_{k_0}\} is admissible. Then for any $m\geq 1$, the set $$\{m(h_j-h_i):\,h_i<h_j\}$$ contains at least one Polignac number