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Taiwan National Olympiad
1997 Taiwan National Olympiad
4
4
Part of
1997 Taiwan National Olympiad
Problems
(1)
fecma numbers
Source: 6-th Taiwanese Mathematical Olympiad 1997
1/17/2007
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
.
number theory proposed
number theory