9 problems

Let $E/\mathbb{Q}$ be an elliptic curve. An elliptic curve over $\mathbb{Q}$ is modular if there exists a primitive Hilbert modular newform over $\mathbb{Q}$ of parallel weight $2$…

Let $m$ and $n$ be positive integers, and let the $m$th and $n$th primes be the primes in those positions in the ordered sequence of primes. Sun's conjecture. Any positive rational…

Let ${\mathbb Q}^+$ denote the positive rational numbers, let ${\mathbb N}$ denote the positive integers, and let ${\cal F}$ be the family of sets under consideration. For…

Let ${\mathbb Q}_{\textup{\textbf{a}}}$ be the common meadow of rational numbers, with an absorbing element for undefined inversion. A datatype defining rewrite system (DDRS) is a…

Let ${\mathbb Q}_0$ be the meadow of rational numbers with totalized inversion. An equational initial algebra specification is a finite set of equations whose initial algebra is…

Let $k\geq 2$ and let $L$ be a regular language of base-$k$ representations of pairs whose quotient set is … A representation in $L$ is a word encoding a pair of nonnegative intege…

Let $k,l\geq 2$ be multiplicatively independent integers. A set $S$ of rational numbers is simultaneously $k$- and $l$-automatic if it is accepted by finite automata in both bases.…

Let $T$ be the recurrence tree generated by the recurrence referred to as (Som4Ord3), and let the generalized Somos-4 sequence be the sequence associated with that recurrence. Prod…

Let $x_1,\ldots,x_n$ be rationals satisfying $|x_1|\leq\cdots\leq|x_n|$, and suppose that for every $y_1,\ldots,y_n\in\mathbb Q$, the implications … and … together imply…