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PEN D Problems
23
D 23
D 23
Source:
May 25, 2007
quadratics
modular arithmetic
Congruences
Problem Statement
Let
p
p
p
be an odd prime of the form
p
=
4
n
+
1
p=4n+1
p
=
4
n
+
1
. [*] Show that
n
n
n
is a quadratic residue
(
m
o
d
p
)
\pmod{p}
(
mod
p
)
. [*] Calculate the value
n
n
n^{n}
n
n
(
m
o
d
p
)
\pmod{p}
(
mod
p
)
.
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