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National and Regional Contests
Taiwan Contests
Taiwan National Olympiad
1997 Taiwan National Olympiad
4
fecma numbers
fecma numbers
Source: 6-th Taiwanese Mathematical Olympiad 1997
January 17, 2007
number theory proposed
number theory
Problem Statement
Let
k
=
2
2
n
+
1
k=2^{2^{n}}+1
k
=
2
2
n
+
1
for some
n
∈
N
n\in\mathbb{N}
n
∈
N
. Show that
k
k
k
is prime iff
k
∣
3
k
−
1
2
+
1
k|3^{\frac{k-1}{2}}+1
k
∣
3
2
k
−
1
+
1
.
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