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2017 PUMaC Team 3
2017 PUMaC Team 3
Source:
September 20, 2019
number theory
Problem Statement
Let
f
(
x
)
=
(
x
−
5
)
(
x
−
12
)
f(x) = (x - 5)(x - 12)
f
(
x
)
=
(
x
−
5
)
(
x
−
12
)
and
g
(
x
)
=
(
x
−
6
)
(
x
−
10
)
g(x) = (x - 6)(x - 10)
g
(
x
)
=
(
x
−
6
)
(
x
−
10
)
. Find the sum of all integers
n
n
n
such that
f
(
g
(
n
)
)
f
(
n
)
2
\frac{f(g(n))}{f(n)^2}
f
(
n
)
2
f
(
g
(
n
))
is defined and an integer.
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