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PEN A Problems
11
A 11
A 11
Source:
May 25, 2007
pigeonhole principle
linear algebra
matrix
modular arithmetic
Divisibility Theory
pen
Problem Statement
Let
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
be integers. Show that the product
(
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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