2 problems

Let $p$ be a prime, let $r$ be a positive integer, and let $d=1,2$, with the first congruence restricted to $p>2$. Guo and Zudilin's conjecture. The preceding supercongruence shoul…

Let $n\equiv 1\pmod{4}$ be a positive integer and let $r\geqslant 1$. Write $(a;q)_k$ for the $q$-shifted factorial, $[m]=(1-q^m)/(1-q)$, and let $\Phi_m(q)$ denote the $m$th cyclo…