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Chile National Olympiad
1995 Chile National Olympiad
1
12 divides (a-b) (a-c) (a-d) (b- c) (b-d) (c-d) (1995 Chile NMO P1)
12 divides (a-b) (a-c) (a-d) (b- c) (b-d) (c-d) (1995 Chile NMO P1)
Source:
November 22, 2021
number theory
divides
divisible
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be integers. Prove that
12
12
12
divides
(
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
)
.
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