Question 86
Let $\mathcal K$ be the integer lattice. Does there exist a bijection $f:\mathbb N\longrightarrow\mathcal K$ such that for every pairwise distinct $a,b,c\in\mathbb N$,
$$\gcd(a,b,c)\gt1\quad\Longrightarrow\quad f(a),f(b),f(c)\text{ are not collinear}?$$
(The integer lattice is the set of plane points with integer coordinates in the Cartesian coordinate system.)
(Stevan Gajović)
$$\gcd(a,b,c)\gt1\quad\Longrightarrow\quad f(a),f(b),f(c)\text{ are not collinear}?$$
(The integer lattice is the set of plane points with integer coordinates in the Cartesian coordinate system.)
(Stevan Gajović)