On certain arithmetic properties of Stern polynomials

Abstract

We prove several theorems concerning arithmetic properties of Stern polynomials defined in the following way: $B_0(t)=0,B_1(t)=1,B_{2n}(t)=t{B}_n(t)$, and $B_{2n+1}(t)=B_n(t)+B_{n+1}(t)$. We study also the sequence $e(n)=\op{deg}_{t}B_{n}(t)$ and give various of its properties.

20 pages