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2012 CHMMC Fall
9
2012 Fall Team #9
2012 Fall Team #9
Source:
March 20, 2022
number theory
Problem Statement
For a positive integer
n
n
n
, let
f
(
n
)
f(n)
f
(
n
)
be equal to
n
n
n
if there is an integer
x
x
x
such that
x
2
−
n
x^2-n
x
2
−
n
is divisible by
2
12
2^{12}
2
12
, and let
f
(
n
)
f(n)
f
(
n
)
be
0
0
0
otherwise. Determine the remainder when
∑
n
=
0
2
12
−
1
f
(
n
)
\sum^{2^{12}-1}_{n=0}f(n)
n
=
0
∑
2
12
−
1
f
(
n
)
is divided by
2
12
2^{12}
2
12
.
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