47 problems

Let $\mathcal{F}$ denote the concatenated Fibonacci constant in base $10$. A real number is normal in base $10$ if every block of $k$ digits occurs with limiting frequency…

Let $\xi$ and $\xi'$ be the cycles associated with Algorithm, and suppose $n\leq4$ and $\|\xi\|>1$. For each modular symbol ${\mathbf v}$ in step A of the algorithm, choose…

Let ${\mathbf v}=[v_1,\dots,v_n]$ be a modular symbol with $\|{\mathbf v}\|>1$, and define … Let $E$ be the standard basis of ${\mathbb Z}^n$. The quadratic form $b({\mathbf v})$ i…

Let ${\mathbf v}=[v_1,\dots,v_n]$ be a modular symbol with $\|{\mathbf v}\|>1$. Define … For a top-dimensional cone $\sigma$ in the Voronoi decomposition containing…

Let $n$ be an integer tested by the algorithm described in the paper, using Fermat and strong Fermat tests and the resulting splittings. Carmichael-recognition algorithm conjecture…

Let $n$ be a positive integer. The query whether $n$ is a Carmichael number is the decision problem of determining whether $n$ is composite and satisfies the defining Carmichael pr…

Non-negligible-prime-ideal conjecture. The proportion of such coefficient vectors is inverse-polynomial in $d$ and $\log(B)$:

Kotnik and van de Lune's conjecture. The smallest counterexample satisfies

Hybrid method pair-count conjecture. The hybrid method considers

For $epsilon>0$, an $epsilon$-unfair polynomial is a 0–1 polynomial having a factor whose relevant unfairness parameter is $epsilon$. Arbitrarily unfair polynomial conjecture. For…

Local-maxima table claim. For every prime $p$ with $2<p\leq19$ and $p\ne17$, the values $M_\beta(p)$ are those given in Table 2, and the corresponding densities $\delta(p)$ of prim…

Let $m$ be a positive integer, let $\mathbb{Q}(\zeta_m+\zeta_m^{-1})$ be the maximal real subfield of the $m$th cyclotomic field, and let $h^+(m)$ denote its class number. Polynomi…

Let $m$ be a positive integer. Write $h(m)$ for the class number of $\mathbb{Q}(\zeta_m)$, let $h^+(m)$ be the class number of its maximal real subfield…

Let $n=pq$ be an RSA modulus, and write $\mathbf{RSA}(n)$ for the problem of breaking RSA and $\mathbf{Fact}(n)$ for the problem of factoring $n$. Write $\mathbf{Rabin}(n)$ for the…

Logarithmic increment conjecture. One has

Let $a,b,d$ be the minimizers of Problem, and let $\mathbf A,\mathbf B\in\mathbb R[[X,Y]]$ be the series associated to $a$ and $b$, respectively. Let $\mathcal C^{[1/3,2/3]}$ and…

The computational refinement of the 1-3-5 conjecture. Except for $m\in\{31,43,111,151,168,200,248,263,319,456,479,871,1752,1864,3544\}$, every such $m$ has a representation for whi…

Absolute PCN-trinomial conjecture. For every integer $m\geq 2$, there exists a bound $T_m$ such that for every prime $p\geq T_m$, there is an absolute PCN-trinomial of degree $m$ o…

Let $q$ be a prime power, let $g(x)\in\mathbb{F}_q[x]$ be a monic polynomial of degree $n$, and let … For $k\in\{1,\ldots,|D|\}$, the $k$-subset sum problem ($k$-SSP) asks whether…

Fix $g$ and let $\eta\in\overline{\mathbb Q}$ be such that $\mathbb Q(\eta)$ is a totally real number field of degree $g$. For sufficiently large prime powers $q=p^n$ with…

Legendre-sequence hardness conjecture. The problem associated with recovering or determining such a Legendre sequence, namely Problem P1 of Damgård, is conjectured to be hard.

Cube-root hardness conjecture. Finding roots for this family is conjectured to be hard, and is conjectured not to be as hard as integer factorization.

Root-finding hardness conjecture. The majority of such polynomials are conjectured to have hard root-finding problems, with hardness not based on integer factorization.

Let $T\in A_5$, and let $C_T$ be the corresponding genus-two curve, with $r(T)$ denoting the rank quantity used in the source. Rational-points conjecture. For $r(T)>1$, the values…

Let $X/{\mathbb F}_q$ be a semiabelian variety and let $Y\subset X$ be a closed subvariety. Let $Z$ be the union of all translates of positive-dimensional semiabelian varieties…