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National and Regional Contests
PEN Problems
PEN D Problems
9
9
Part of
PEN D Problems
Problems
(1)
D 9
Source:
5/25/2007
Show that there exists a composite number
n
n
n
such that
a
n
≡
a
(
m
o
d
n
)
a^n \equiv a \; \pmod{n}
a
n
≡
a
(
mod
n
)
for all
a
∈
Z
a \in \mathbb{Z}
a
∈
Z
.
modular arithmetic
Congruences