# Ring problem with zero divisors

#### ashamrock415

Does every ring with 1001 elements contain zero divisors?

#### tonio

Does every ring with 1001 elements contain zero divisors?

Yes, otherwise it'd be a field - a finite ring without zero divisors is a division ring and thus a field (this is not trivial!) - , but $$\displaystyle 1001=7\cdot 11\cdot 13$$ is not the power of a prime...

Tonio