What is the least positive integer $n$ such that $n^2 - n$ is divisible by some but not all integer values of $k$ when $1\leq k \leq n$?
Question:
What is the least positive integer $n$ such that $n^2 - n$ is divisible by some but not all integer values of $k$ when $1\leq k \leq n$?
Answer:
Let's think step by step.

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What is the least positive integer $n$ such that $n^2 - n$ is divisible by some but not all integer values of $k$ when $1\leq k \leq n$?
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