MathDB

Determine whether there exist

100

disks

D_2,D_3,\ldots ,D_{101}

in the plane such that the following conditions hold for all pairs

(a,b)

of indices satisfying

2\le a< b\le 101

:
[*] If

a|b

then

D_a

is contained in

D_b

. [*] If

\gcd (a,b)=1

then

D_a

and

D_b

are disjoint.
(A disk

D(O,r)

is a set of points in the plane whose distance to a given point

O

is at most a given positive real number

r

Problem Statement