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Baltic Way
2007 Baltic Way
20
20
Part of
2007 Baltic Way
Problems
(1)
ab is a perfect cube if ab(a-b) divides a^3+b^3+ab
Source: Baltic Way 2007
11/30/2010
Let
a
a
a
and
b
b
b
be positive integers,
b
<
a
b<a
b
<
a
, such that
a
3
+
b
3
+
a
b
a^3+b^3+ab
a
3
+
b
3
+
ab
is divisible by
a
b
(
a
ā
b
)
ab(a-b)
ab
(
a
ā
b
)
. Prove that
a
b
ab
ab
is a perfect cube.
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