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11.2
8| ](\sqrt{3}{n}+\sqrt{3}{n+2})^3]+1
8| ](\sqrt{3}{n}+\sqrt{3}{n+2})^3]+1
Source:
August 26, 2024
number theory
divides
divisible
Problem Statement
Prove that, for every integer
n
>
2
n > 2
n
>
2
, the number
[
(
n
3
+
n
+
2
3
)
3
]
+
1
\left[\left( \sqrt[3]{n}+\sqrt[3]{n+2}\right)^3\right]+1
[
(
3
n
+
3
n
+
2
)
3
]
+
1
is divisible by
8
8
8
.
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