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PEN B Problems
6
B 6
B 6
Source:
May 25, 2007
modular arithmetic
number theory
relatively prime
Primitive Roots
Problem Statement
Suppose that
m
m
m
does not have a primitive root. Show that
a
ϕ
(
m
)
2
≡
1
(
m
o
d
m
)
a^{ \frac{\phi(m)}{2}}\equiv 1 \; \pmod{m}
a
2
ϕ
(
m
)
≡
1
(
mod
m
)
for every
a
a
a
relatively prime
m
m
m
.
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