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# divisibility problem solving help please

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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

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By simple calculation, the smallest n that works is n = 6.

Feb 2, 2021
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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