All eight integers are the same modulo 2005
Posted: Sun Jan 10, 2021 1:12 pm
At each corner of a cube, an integer is written. A $legal$
$transition$ of the cube consists in picking any corner of the cube and adding the value written at that corner to the value written at some adjacent corner. Prove that there is a finite sequence of $legal$ $transitions$ of the given cube such that $8$ integers written are all the same modulo $2005$.
$transition$ of the cube consists in picking any corner of the cube and adding the value written at that corner to the value written at some adjacent corner. Prove that there is a finite sequence of $legal$ $transitions$ of the given cube such that $8$ integers written are all the same modulo $2005$.