3 problems

A rational number $p/q$ has an antipalindromic quotient representation if there are antipalindromic numbers $A$ and $B$ such that $p/q=A/B$. Rational antipalindromic quotient conje…

Let $p>1$ be odd. A rational number $p/q$ has a palindromic quotient representation if there are palindromic numbers $A$ and $B$ such that $p/q=A/B$. Odd rational palindrome quotie…

Let $F$ be the field in which rational representations of $GL_2(F)$ are considered, and let $\underleftarrow{\mathcal{C}}_p(F)\operatorname{-mod}$ denote the corresponding module c…