9 problems

Let $E$ be a moiety of a primitive Eisenstein circle packing. A positive integer is called sporadic if it is admissible in $E$, does not appear in $E$, and does not belong to one o…

Let $E$) be a moiety of a bounded primitive Eisenstein circle packing. Let $N$ be a positive real number, and let $c_E$ denote a constant depending on $E$. Let…

Parker, Rushall and Hunt's conjecture. Every odd norm-perfect Eisenstein integer has the form

Let $\beta=a+b\alpha$ and $\beta'=a'+b'\alpha$ be primitive Eisenstein integers, and write $\beta\preceq\beta'$ when $b\leq b'$. Let $\beta$ be a Fibonacci Eisenstein integer, let…

Let ${\cal G}_n$ be an infinite sequence of distinct colorings of primitive sphere triangulations with degree sequence $6,\ldots,6,2,2,2$. For a coloring ${\cal C}$, let…

Let $k$ be a nonnegative integer, and let … Fermat's representation conjecture. If $k$ is a prime number congruent to $1$ modulo $3$, then … This conjecture was proved by Euler in…

Odd-power classification conjecture. There is a quasigroup isomorphism

Terai–Takakuwa's conjecture. When $\gcd(a,b)=1$, the unique solution is $(x,y,z)=(1,1,2)$. The source reports this as a conjecture arising from the Eisenstein-number analogue of Je…

Odd norm-perfect form conjecture. The integer $\alpha$ must have the form