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239 Open Math Olympiad
2012 239 Open Mathematical Olympiad
2
2
Part of
2012 239 Open Mathematical Olympiad
Problems
(1)
Composite sum
Source: 239 2012 S2
7/30/2020
Natural numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
are given such that
c
>
b
c>b
c
>
b
. Prove that if
a
+
b
+
c
+
d
=
a
b
ā
c
d
a + b + c + d = ab-cd
a
+
b
+
c
+
d
=
ab
ā
c
d
, then
a
+
c
a + c
a
+
c
is a composite number.
number theory