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PEN Problems
PEN D Problems
10
10
Part of
PEN D Problems
Problems
(1)
D 10
Source:
5/25/2007
Let
p
p
p
be a prime number of the form
4
k
+
1
4k+1
4
k
+
1
. Suppose that
2
p
+
1
2p+1
2
p
+
1
is prime. Show that there is no
k
∈
N
k \in \mathbb{N}
k
∈
N
with
k
<
2
p
k<2p
k
<
2
p
and
2
k
≡
1
(
m
o
d
2
p
+
1
)
2^k \equiv 1 \; \pmod{2p+1}
2
k
≡
1
(
mod
2
p
+
1
)
.
modular arithmetic
quadratics
Congruences