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4
4
Part of
1989 AIME Problems
Problems
(1)
Arithmetic Series Practice
Source:
2/19/2006
If
a
<
b
<
c
<
d
<
e
a<b<c<d<e
a
<
b
<
c
<
d
<
e
are consecutive positive integers such that
b
+
c
+
d
b+c+d
b
+
c
+
d
is a perfect square and
a
+
b
+
c
+
d
+
e
a+b+c+d+e
a
+
b
+
c
+
d
+
e
is a perfect cube, what is the smallest possible value of
c
c
c
?
geometry
3D geometry