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Austria Contests
Austrian MO National Competition
1991 Federal Competition For Advanced Students
1
old exercise
old exercise
Source: Austria 1991
July 10, 2009
number theory proposed
number theory
Problem Statement
Suppose that
a
,
b
,
a,b,
a
,
b
,
and \sqrt[3]{a}\plus{}\sqrt[3]{b} are rational numbers. Prove that
a
3
\sqrt[3]{a}
3
a
ā
and
b
3
\sqrt[3]{b}
3
b
ā
are also rational.
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