13 problems

Let $E$ be a fixed elliptic curve over $\mathbb{Q}$, let $P\in E(\mathbb{Q})$ be a rational point, and let $m$ be the fixed integer indexing the generalized elliptic Fermat numbers…

Let $(A_n)$ be the Somos-4 sequence referred to in the source, and for a prime $p$ let the gap length be the distance between successive terms of the sequence divisible by $p$. Rob…

Let ${\mathcal W}=(W_n)_{n\ge0}$ be an elliptic divisibility sequence and let $p$ be a prime. For an exponent $N=N_p\ge1$, consider the subsequences indexed by $mp^{kN}$ for each…

Bounded-length conjecture. If the length of $B_n$ is bounded, then $n$ is bounded. Moreover, provided that $E$ is in minimal form, the bound depends only on the length and not on…

Let $(W_n)$ be an unbounded elliptic divisibility sequence and let $p$ be a prime. Suppose there is an exponent $e\geq 1$ such that, for each $0\leq i<e$, the limit … exists in…

Let $E_a$ be the elliptic curve considered above, let $P$ be a non-torsion point in $E_a(\mathbb{Q})$, and let $B_n(E_a,P)$ denote the associated elliptic divisibility sequence. Pr…

Let $E$ be a fixed elliptic curve over $\mathbb{Q}$, let $P\in E(\mathbb{Q})$ be a rational point, and let $F=(F_n)_{n\in\mathbb{N}}$ be the associated sequence of elliptic Fermat…

Let $D=(D_n)_{n\in\mathbb{N}}$ be an elliptic divisibility sequence. Primality conjecture. The sequence $D$ contains only finitely many prime terms. Everest, Miller, and Stephens p…

Let $E/\mathbb{Q}$ be an elliptic curve given by a Weierstrass equation, let $P\in E(\mathbb{Q})$ be a nontorsion point, and write … as a fraction in lowest terms. The resulting in…

Let $(C_m)$ be the sequence whose odd terms arise in the example under discussion, and suppose that these odd terms form an elliptic divisibility sequence. Prime-term finiteness co…

Let $D\in\mathbb{Z}$ be non-zero, and let $E:y^2=x^3+D$. For a rational point $P\in E(\mathbb{Q})$, write $B_P$ for the denominator associated to $P$ in the elliptic divisibility s…

Primality conjecture. Only finitely many multiples of $P$ have a prime-power denominator in their $x$-coordinate.

Let $B=(B_n)$ be an elliptic divisibility sequence generated by a rational point on an elliptic curve in minimal form. A prime term is a term $B_n/B_1$ that is prime. The uniform p…