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CHMMC problems
2013 CHMMC (Fall)
3
2013 Fall Team #3
2013 Fall Team #3
Source:
March 26, 2022
algebra
Problem Statement
Let
p
n
p_n
p
n
be the product of the
n
n
n
th roots of
1
1
1
. For integral
x
>
4
x > 4
x
>
4
, let
f
(
x
)
=
p
1
−
p
2
+
p
3
−
p
4
+
.
.
.
+
(
−
1
)
x
+
1
p
x
f(x) = p_1 - p_2 + p_3 - p_4 + ... + (-1)^{x+1}p_x
f
(
x
)
=
p
1
−
p
2
+
p
3
−
p
4
+
...
+
(
−
1
)
x
+
1
p
x
. What is
f
(
2010
)
f(2010)
f
(
2010
)
?
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