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2
E 2
E 2
Source:
May 25, 2007
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Problem Statement
Let
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
be integers with
a
>
b
>
c
>
d
>
0
a>b>c>d>0
a
>
b
>
c
>
d
>
0
. Suppose that
a
c
+
b
d
=
(
b
+
d
+
a
−
c
)
(
b
+
d
−
a
+
c
)
ac+bd=(b+d+a-c)(b+d-a+c)
a
c
+
b
d
=
(
b
+
d
+
a
−
c
)
(
b
+
d
−
a
+
c
)
. Prove that
a
b
+
c
d
ab+cd
ab
+
c
d
is not prime.
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