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+1
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avatar+255 

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?

 Dec 15, 2019
 #1
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+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.

 Dec 15, 2019
 #2
avatar+255 
+2

OH WAIT NO I THINK IT'S FIVE BECAUSE YOU SAY DO THE SAME THING FOR THAT because 20 isn't divisible by 3!!! thanks for giving me your idea though!

atlas9  Dec 15, 2019
 #3
avatar+109518 
+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!

 Dec 15, 2019
 #4
avatar+109518 
+2

Give yourself a point atlas9.  You worked it out!    cool

 Dec 15, 2019

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