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 $2005$.
All eight integers are the same modulo 2005
- Enthurelxyz
- Posts:17
- Joined:Sat Dec 05, 2020 10:45 pm
- Location:Bangladesh
- Contact:
and miles to go before we sleep
and miles to go before we sleep
and miles to go before we sleep
- Mehrab4226
- Posts:230
- Joined:Sat Jan 11, 2020 1:38 pm
- Location:Dhaka, Bangladesh
Re: All eight integers are the same modulo 2005
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré
-Henri Poincaré