i feel like this is supposed to be super easy, but i can't figure it out.. :(

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 ≤ k ≤ n?

atlas9 Dec 15, 2019

#1**+1 **

I think the answer is n = 6. For n = 6, n^2 - n = 30, which is divisible by 1, 2, 3, 5, and 6, but not 4.

Guest Dec 15, 2019

#3**+3 **

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 ≤ k ≤ n?

If n=2 then 2^2-2=2 2 is divisable by 2 so wouldn't that be ok? Oh no it is not ok ... I get it

If n=3 then 3^2-3=6 6 is divisable by 1,2,3 so that is no good either

If n=4 then 4^2-4=12 12 is divisable by 1,2,3 and 4 no good

If n=5 then 5^2-5=20 20 is divisable by 1,2,4, and 5 BUT not 3.

so your answer of n=5 is spot on!

Melody Dec 15, 2019