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Prove that product is a perfect cube...
Prove that product is a perfect cube...
Source:
December 9, 2010
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number theory unsolved
number theory
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be integers such that
a
b
+
b
c
+
c
a
=
3
\frac ab+\frac bc+\frac ca= 3
b
a
+
c
b
+
a
c
=
3
Prove that
a
b
c
abc
ab
c
is a cube of an integer.
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