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PEN A Problems
73
A 73
A 73
Source:
May 25, 2007
number theory
Divisibility Theory
pen
Problem Statement
Determine all pairs
(
n
,
p
)
(n,p)
(
n
,
p
)
of positive integers such that [*]
p
p
p
is a prime,
n
>
1
n>1
n
>
1
, [*]
(
p
−
1
)
n
+
1
(p-1)^{n} + 1
(
p
−
1
)
n
+
1
is divisible by
n
p
−
1
n^{p-1}
n
p
−
1
.
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