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9
2016 Discrete #9
2016 Discrete #9
Source:
August 10, 2022
2016
Discrete Math Test
Problem Statement
Define
ϕ
n
(
x
)
\phi_n(x)
ϕ
n
(
x
)
to be the number of integers
y
y
y
less than or equal to
n
n
n
such that
gcd
(
x
,
y
)
=
1
\gcd(x,y)=1
g
cd
(
x
,
y
)
=
1
. Also, define
m
=
lcm
(
2016
,
6102
)
m=\text{lcm}(2016,6102)
m
=
lcm
(
2016
,
6102
)
. Compute
ϕ
m
m
(
2016
)
ϕ
m
m
(
6102
)
.
\frac{\phi_{m^m}(2016)}{\phi_{m^m}(6102)}.
ϕ
m
m
(
6102
)
ϕ
m
m
(
2016
)
.
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