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2007 Balkan MO Shortlist
N3
N3
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2007 Balkan MO Shortlist
Problems
(1)
bulgaria tst 2007
Source:
3/31/2011
i thought that this problem was in mathlinks but when i searched i didn't find it.so here it is: Find all positive integers m for which for all
α
,
β
∈
Z
−
{
0
}
\alpha,\beta \in \mathbb{Z}-\{0\}
α
,
β
∈
Z
−
{
0
}
2
m
α
m
−
(
α
+
β
)
m
−
(
α
−
β
)
m
3
α
2
+
β
2
∈
Z
\frac{2^m \alpha^m-(\alpha+\beta)^m-(\alpha-\beta)^m}{3 \alpha^2+\beta^2} \in \mathbb{Z}
3
α
2
+
β
2
2
m
α
m
−
(
α
+
β
)
m
−
(
α
−
β
)
m
∈
Z
algebra
polynomial
trigonometry
algebra proposed