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Putnam 2011 B6

Source:

December 5, 2011
Putnamalgebrapolynomialcollege contests

Problem Statement

Let pp be an odd prime. Show that for at least (p+1)/2(p+1)/2 values of nn in {0,1,2,…,p−1},\{0,1,2,\dots,p-1\}, \sum_{k=0}^{p-1}k!n^k   \text{is not divisible by }p.
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