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Netherlands Contests
Dutch Mathematical Olympiad
2012 Dutch Mathematical Olympiad
1
(a-b)(a-c)(a-d)(b-c)(b-d)(c-d) is divisible by 12
(a-b)(a-c)(a-d)(b-c)(b-d)(c-d) is divisible by 12
Source: Dutch NMO 2012 p1
September 6, 2019
divisible
number theory
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
, and
d
d
d
be four distinct integers. Prove that
(
a
−
b
)
(
a
−
c
)
(
a
−
d
)
(
b
−
c
)
(
b
−
d
)
(
c
−
d
)
(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)
(
a
−
b
)
(
a
−
c
)
(
a
−
d
)
(
b
−
c
)
(
b
−
d
)
(
c
−
d
)
is divisible by
12
12
12
.
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