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2012 CHMMC Spring
1
2012 Spring Team #1
2012 Spring Team #1
Source:
March 20, 2022
number theory
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive integers. Suppose that
(
a
+
b
)
(
a
+
c
)
=
77
(a + b)(a + c) = 77
(
a
+
b
)
(
a
+
c
)
=
77
and
(
a
+
b
)
(
b
+
c
)
=
56
(a + b)(b + c) = 56
(
a
+
b
)
(
b
+
c
)
=
56
. Find
(
a
+
c
)
(
b
+
c
)
(a + c)(b + c)
(
a
+
c
)
(
b
+
c
)
.
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