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2005 Greece Junior Math Olympiad
4
Find nonzero integers.
Find nonzero integers.
Source: 22nd Hellenic Jounior mo , 2005 , prb4.
November 17, 2005
Problem Statement
Find all nonzero integers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
with
a
>
b
>
c
>
d
a>b>c>d
a
>
b
>
c
>
d
that satisfy
a
b
+
c
d
=
34
ab+cd=34
ab
+
c
d
=
34
and
a
c
ā
b
d
=
19.
ac-bd=19.
a
c
ā
b
d
=
19.
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