Cyclic Permutations of Five-Digit Numbers Divisible by 41

Let $N$ be a five-digit number that is divisible by 41. Prove that any cyclic permutation of the digits of $N$ is also divisible by 41.

For example, if $N = 93,767$ is divisible by 41, then conclude that the cyclic permutation $37,679$ is also divisible by 41.