3 problems

Let $V_n$ be the Apéry-like sequence … For a prime $p>3$, the first author's conjecture asserts First author's conjecture. … The case $p\equiv1\pmod4$ is verified in the paper, whe…

Let $p\ge 5$ be a prime, and let $\\{u_n\\}_{n\ge 0}$ be one of the sequences $\mathbf{B}$ and $\mathbf{F}$, defined by … or … Here $\left(\frac{p}{3}\right)$ is the Legendre symbo…

Let … and write its Taylor expansion as … This is the Askey–Gasper rational function. Askey–Gasper coefficient supercongruence. For every prime $p\geqslant 5$ and integer…