number theorygreatest common divisormodular arithmetic
Problem Statement
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