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Moldova Contests
EGMO TST - Moldova
2023 Moldova EGMO TST
1
n=(ab-cd)\cdot(bc-ad)\cdot(ca-bd)
n=(ab-cd)\cdot(bc-ad)\cdot(ca-bd)
Source: Moldova EGMO TST 2023
February 4, 2023
Problem Statement
Integers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
satisfy
a
+
b
+
c
+
d
=
0
a+b+c+d=0
a
+
b
+
c
+
d
=
0
. Show that
n
=
(
a
b
−
c
d
)
⋅
(
b
c
−
a
d
)
⋅
(
c
a
−
b
d
)
n=(ab-cd)\cdot(bc-ad)\cdot(ca-bd)
n
=
(
ab
−
c
d
)
⋅
(
b
c
−
a
d
)
⋅
(
c
a
−
b
d
)
is a perfect square.
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