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Mathematics
Problem
Show that the number
n
(
n
+
1
)
2
\dfrac{n(n+1)}{2}
2
n
(
n
+
1
)
is divisible by
3
3
3
whenever
n
≡
0
(
m
o
d
3
)
n\equiv0\pmod{3}
n
≡
0
(
mod
3
)
or
n
≡
2
(
m
o
d
3
)
n\equiv2\pmod{3}
n
≡
2
(
mod
3
)
.
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