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New Zealand Contests
NZMOC Camp Selection Problems
2018 NZMOC Camp Selection Problems
1
1
Part of
2018 NZMOC Camp Selection Problems
Problems
(1)
(a - b)(a - c)(a - d)(b - c)(b - d)(c - d) is multiple of 12
Source: New Zealand NZMOC Camp Selection Problems 2018 p1
9/19/2021
Suppose that
a
,
b
,
c
a, b, c
a
,
b
,
c
and
d
d
d
are four different integers. Explain why
(
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
)
must be a multiple of
12
12
12
.
multiple
divides
number theory