Divisor Nim is an impartial game in which a move subtracts a positive number of stones from one heap, with the requirement that this number divide the size of every other heap. The number removed need not divide the size of the heap being changed. Empty heaps impose no restriction, since every positive integer divides 0. The player with no legal move loses.
If 
is the smallest nonempty heap
of a nonterminal position 
,
then its nim-value 
satisfies
 |
where 
is the floor
function (Tyagi 2026). The bound is independent of
the number and sizes of the other heaps.
from 
-Pile
Divisor Nim." 3 Oct 2026.