Math camp qualifying quiz 2014 Problem 5

Nov 2014
3
0
Amherst, MA
Hi I am hoping to participate in a math camp for gifted students next summer. In order to go there I have to pass a qualifying test that will be released soon. In the meantime I have the test from last year to practice with and I am really struggling with it. Any help would be greatly appreciated.

5. Let p be a prime. For which integers n is it possible to split the set {1, 2, . . . , n} into p disjoint subsets such that the sum
of the integers in each of the subsets is the same? Prove your answer.
 
Jun 2014
945
191
Earth
Hi I am hoping to participate in a math camp for gifted students next summer. In order to go there I have to pass a qualifying test
that will be released soon. In the meantime I have the test from last year to practice with and I am really struggling with it.
Any help would be greatly appreciated.

5. Let p be a prime. For which integers n is it possible to split the set {1, 2, . . . , n} into p disjoint subsets such that the sum
of the integers in each of the subsets is the same? Prove your answer.
If you're really gifted, then you need to demonstrate it here. Show some of your attempts here.
If you can't even show some of what you know about what you know here, then you're
probably not ready to pass that qualifying for that math camp. And you shouldn't go to the math camp.