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1994 Romania TST for IMO
2:
Divisible by $((n-1)^n+1)^2$ (Romania TST 1994)
Divisible by $((n-1)^n+1)^2$ (Romania TST 1994)
Source: Romania TST 1994
August 4, 2009
modular arithmetic
number theory proposed
number theory
Problem Statement
Let
n
n
n
be an odd positive integer. Prove that
(
(
n
−
1
)
n
+
1
)
2
((n-1)^n+1)^2
((
n
−
1
)
n
+
1
)
2
divides
n
(
n
−
1
)
(
n
−
1
)
n
+
1
+
n
n(n-1)^{(n-1)^n+1}+n
n
(
n
−
1
)
(
n
−
1
)
n
+
1
+
n
.
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