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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 \(1\leq k \leq n\)?

 Feb 2, 2021
 #1
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By simple calculation, the smallest n that works is n = 6.

 Feb 2, 2021
 #2
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I originally went with n = 2 but I had overlooked the "but not all integer values" stipulation.  So never mind. 

 Feb 2, 2021
edited by Guest  Feb 2, 2021

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