3 problems

Let … where the polynomials satisfy $P_0(q)=1$, $P_1(q)=q+1$, $P_2(q)=q^3+q^2+q+1$, and $P_n(q)=(1+q^n)P_{n-1}(q)+qP_{n-2}(q)-qP_{n-3}(q)$ for $n\geq3$. Let $\mathrm T_1(N,M;q)$ de…

Composite-index conjecture. For no composite integer $n>1$ does

Let $T_{2k}(b,1)$ be the trinomial coefficient polynomial used in the paper. Consider identities … where $a_0,a_1,m\in\mathbb Z$, $b\in\{1,3,4,\ldots\}$, $a_1>0$, and $C^2$ is posi…