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PEN H Problems
25
H 25
H 25
Source:
May 25, 2007
geometry
3D geometry
modular arithmetic
Diophantine Equations
pen
Problem Statement
What is the smallest positive integer
t
t
t
such that there exist integers
x
1
,
x
2
,
⋯
,
x
t
x_{1},x_{2}, \cdots, x_{t}
x
1
,
x
2
,
⋯
,
x
t
with
x
1
3
+
x
2
3
+
⋯
+
x
t
3
=
200
2
2002
?
{x_{1}}^{3}+{x_{2}}^{3}+\cdots+{x_{t}}^{3}=2002^{2002}\;\;?
x
1
3
+
x
2
3
+
⋯
+
x
t
3
=
200
2
2002
?
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