11.2

Part of 1993 All-Russian Olympiad Regional Round

Problems(1)

8| ](\sqrt{3}{n}+\sqrt{3}{n+2})^3]+1

Source:

Prove that, for every integer

n > 2

\left[\left( \sqrt[3]{n}+\sqrt[3]{n+2}\right)^3\right]+1

is divisible by

8

number theorydividesdivisible