6 problems

For a prime $p$, let $(T_n)$ be the Tribonacci sequence defined by … with $T_0=0$ and $T_1=T_2=1$, and let $up$ denote the $p$-adic valuation. Marques–Lengyel conjecture. The…

Let $\mathcal{ML}$ be the set of primes $p$ for which the Marques–Lengyel conjecture holds, and let $\mathcal{NMLR}$ be the set of primes for which the rational-center variant fail…

Let $p$ be a prime number, and let $T(n)$ be the Tribonacci sequence defined by $T(0)=0$, $T(1)=T(2)=1$, and $T(n+3)=T(n+2)+T(n+1)+T(n)$. Write $\nu_p(m)$ for the exponent of $p$ i…

Let $p$) be a prime number, and let $T(n)$ be the Tribonacci sequence defined by $T(0)=0$, $T(1)=T(2)=1$, and $T(n+3)=T(n+2)+T(n+1)+T(n)$. Write $up(m)$ for the exponent of $p$ in…

For each weight $n$, let $\mathsf{AMTV}_n$ denote the rational vector space of alternating multiple two-one values of weight $n$. Tribonacci dimension conjecture. The generating fu…

Let $(T_n)_{n\ge 1}$ be the Tribonacci sequence defined by … A Diophantine triple with values in the Tribonacci sequence is a triple of positive integers $a<b<c$ such that $ab+1$,…