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1969 IMO Shortlist
34
34
Part of
1969 IMO Shortlist
Problems
(1)
Divisibility problem by a^2+ab+b^2
Source:
9/29/2010
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N
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(HUN 1)
(
H
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Let
a
a
a
and
b
b
b
be arbitrary integers. Prove that if
k
k
k
is an integer not divisible by
3
3
3
, then
(
a
+
b
)
2
k
+
a
2
k
+
b
2
k
(a + b)^{2k}+ a^{2k} +b^{2k}
(
a
+
b
)
2
k
+
a
2
k
+
b
2
k
is divisible by
a
2
+
a
b
+
b
2
a^2 +ab+ b^2
a
2
+
ab
+
b
2
number theory
Divisibility
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