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2010 Balkan MO Shortlist
N1
N1
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2010 Balkan MO Shortlist
Problems
(1)
Dividing $\mathbb{Z}$ into triples with square
Source: Balkan-2010 Shortlist
8/16/2018
Determine whether it is possible to partition
Z
\mathbb{Z}
Z
into triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
such that, for every triple,
∣
a
3
b
+
b
3
c
+
c
3
a
∣
|a^3b + b^3c + c^3a|
∣
a
3
b
+
b
3
c
+
c
3
a
∣
is perfect square.
number theory