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Moldova Contests
JBMO TST - Moldova
2013 Junior Balkan Team Selection Tests - Moldova
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Part of
2013 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
Number Theory
Source: Moldova JTST 2013
2/28/2020
Given are positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that
a
a
a
is odd,
b
>
c
b>c
b
>
c
,
a
,
b
,
c
a, b, c
a
,
b
,
c
are coprime and
a
(
b
ā
c
)
=
2
b
c
a(b-c) =2bc
a
(
b
ā
c
)
=
2
b
c
. Prove that
a
b
c
abc
ab
c
is square
number theory