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2016 JBMO Shortlist
5
(a + b)(a + c)(a + d)(b + c)(b + d)(c + d) =\overline{abcd}
(a + b)(a + c)(a + d)(b + c)(b + d)(c + d) =\overline{abcd}
Source: JBMO 2016 Shortlist N5
October 14, 2017
JBMO
number theory
Problem Statement
Determine all four-digit numbers
a
b
c
d
‾
\overline{abcd}
ab
c
d
such that
(
a
+
b
)
(
a
+
c
)
(
a
+
d
)
(
b
+
c
)
(
b
+
d
)
(
c
+
d
)
=
a
b
c
d
‾
(a + b)(a + c)(a + d)(b + c)(b + d)(c + d) =\overline{abcd}
(
a
+
b
)
(
a
+
c
)
(
a
+
d
)
(
b
+
c
)
(
b
+
d
)
(
c
+
d
)
=
ab
c
d
:
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