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National and Regional Contests
PEN Problems
PEN A Problems
13
13
Part of
PEN A Problems
Problems
(1)
A 13
Source:
5/25/2007
Show that for all prime numbers
p
p
p
,
Q
(
p
)
=
∏
k
=
1
p
−
1
k
2
k
−
p
−
1
Q(p)=\prod^{p-1}_{k=1}k^{2k-p-1}
Q
(
p
)
=
k
=
1
∏
p
−
1
k
2
k
−
p
−
1
is an integer.
floor function
logarithms
inequalities
Divisibility Theory