The largest of the following integers which divides each of the numbers of the sequence 1^5 \minus{} 1,\, 2^5 \minus{} 2,\, 3^5 \minus{} 3,\, \cdots, n^5 \minus{} n, \cdots is:
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 60<spanclass=′latex−bold′>(C)</span> 15<spanclass=′latex−bold′>(D)</span> 120<spanclass=′latex−bold′>(E)</span> 30 number theorygreatest common divisormodular arithmetic