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CIIM
2018 CIIM
Problem 3
Problem 3
Part of
2018 CIIM
Problems
(1)
CIIM 2018 Problem 3
Source:
3/9/2019
Let
m
m
m
be an integer and
Z
m
\mathbb{Z}_m
Z
m
the set of integer modulo
m
m
m
. An equivalence relation is defined in
Z
m
\mathbb{Z}_m
Z
m
given by,
x
∼
y
x \sim y
x
∼
y
if there exists a natural
t
t
t
such that
y
≡
2
t
x
(
m
o
d
m
)
y \equiv 2^tx \, (\bmod m)
y
≡
2
t
x
(
mod
m
)
. Find al values of
m
m
m
such that the number of equivalent classes is even.
CIIM2018
undergraduate