IIMB 2002 (QA) PYQs

Find the smallest positive integer $n$ such that $2^n -1$ is divisible by 3, 5, and 7.

Let $n$ be a positive integer. Which of the following statements is true about $n$ if $n^{3}-n$ is divisible by $6$ ?

What is the minimum number that, when added to $9454351626$, results in a sum that is divisible by $11$?