7 problems

Let $n$ be a positive odd integer, let $(a;q)_k$ denote the $q$-shifted factorial, and let $\Phi_n(q)$ be the $n$th cyclotomic polynomial. Guo's conjecture. Modulo $\Phi_n(q)^2$, t…

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…

Let $n \equiv 1\pmod{4}$ be a positive integer. Define the $q$-integer $[m]=(1-q^m)/(1-q)$, the $q$-shifted factorial $(a;q)k=\prod{j=0}^{k-1}(1-aq^j)$, and let $Phin(q)$ denote the…

Let $n$ be a positive integer with $n\equiv3\pmod4$, let $[n]=(1-q^n)/(1-q)$, let $(a;q)_k$ be the $q$-shifted factorial, and let $(a_1,\ldots,a_r;q)_k=\prod_{i=1}^r(a_i;q)_k$. Set…

Let $p,m,r$ satisfy the hypotheses of the source's Theorem 2k2k2k-1. Further q-supercongruence conjecture. … The supplied text contains only the cross-reference to the theorem's hy…

Let the congruences denoted by (new-RV2)--(new-RV4) be the three earlier q-supercongruences referenced by the source. Strengthening conjecture. Those congruences also hold modulo…

Let $p$ be an odd prime, let $m,r$ be positive integers with $p\nmid m$, and let $s\leqslant p-1$ be nonnegative. Write $\langle a\rangle_p$ for the least nonnegative residue of…