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PEN Problems
PEN O Problems
28
28
Part of
PEN O Problems
Problems
(1)
O 28
Source:
5/25/2007
Prove that the set of positive integers cannot be partitioned into three nonempty subsets such that, for any two integers
x
x
x
,
y
y
y
taken from two different subsets, the number
x
2
ā
x
y
+
y
2
x^{2}-xy+y^{2}
x
2
ā
x
y
+
y
2
belongs to the third subset.