roles) || in_array('administrator', $user->roles) || in_array('admin', $user->roles ) ) { ?>
probname); ?>
Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>
Topics: nid, "Topics"); ?> Prerequisites: nid, "Prerequisites"); ?>
Supplies: nid, "Supplies"); ?> Pedagogy: nid, "Pedagogy"); ?>
Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
1-2
3-4
 
 
 
5-6
 
 
7-8
 
9-10
11-12
13-14
Solution: nid, "Solution"); ?>
Problem

``Sums and Cubes III.'' The following gem is due to Ross Honsberger.

The first $n$ positive integers are not the only set of numbers with the property that the sum of their cubes is equal to the square of their sum. Choose any two-digit number $N$, preferably not prime. Then list all the positive divisors of this number, including 1 and $N$. Finally, underneath each number in this list tally how many positive divisors it has, thereby creating a new list of equal length. Then this new list has the desired property. For example, the divisors of 6 are 1, 2, 3, and 6; which have 1, 2, 2, and 4 positive divisors, respectively. Sure enough, $1^3+2^3+2^3+4^3=81=(1+2+2+4)^2$.

Details
Source Title: Circle in a Box
Authors
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References
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'; } ?>
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Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
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DEFINITIONS
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