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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
72
72
Part of
PEN A Problems
Problems
(1)
A 72
Source:
5/25/2007
Determine all pairs
(
n
,
p
)
(n,p)
(
n
,
p
)
of nonnegative integers such that [*]
p
p
p
is a prime, [*]
n
<
2
p
n<2p
n
<
2
p
, [*]
(
p
−
1
)
n
+
1
(p-1)^{n} + 1
(
p
−
1
)
n
+
1
is divisible by
n
p
−
1
n^{p-1}
n
p
−
1
.
modular arithmetic
number theory
Divisibility Theory