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1
7 / abc + (7 - a)(7 - b)(7 - c) when a,b,c \in {1,...,6} (HOMC 2009 J Q1)
7 / abc + (7 - a)(7 - b)(7 - c) when a,b,c \in {1,...,6} (HOMC 2009 J Q1)
Source:
July 25, 2019
number theory
divisible
Problem Statement
Let
a
,
b
,
c
a,b, c
a
,
b
,
c
be
3
3
3
distinct numbers from
{
1
,
2
,
3
,
4
,
5
,
6
}
\{1, 2,3, 4, 5, 6\}
{
1
,
2
,
3
,
4
,
5
,
6
}
Show that
7
7
7
divides
a
b
c
+
(
7
−
a
)
(
7
−
b
)
(
7
−
c
)
abc + (7 - a)(7 - b)(7 - c)
ab
c
+
(
7
−
a
)
(
7
−
b
)
(
7
−
c
)
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