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Putnam
2011 Putnam
B6
B6
Part of
2011 Putnam
Problems
(1)
Putnam 2011 B6
Source:
12/5/2011
Let
p
p
p
be an odd prime. Show that for at least
(
p
+
1
)
/
2
(p+1)/2
(
p
+
1
)
/2
values of
n
n
n
in
{
0
,
1
,
2
,
…
,
p
−
1
}
,
\{0,1,2,\dots,p-1\},
{
0
,
1
,
2
,
…
,
p
−
1
}
,
\sum_{k=0}^{p-1}k!n^k \text{is not divisible by }p.
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