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Challenge problem

• To: mathgroup at smc.vnet.net
• Subject: [mg71123] Challenge problem
• From: "Coleman, Mark" <Mark.Coleman at LibertyMutual.com>
• Date: Thu, 9 Nov 2006 03:37:21 -0500 (EST)

I recently received the annual newsletter from the Math-Stats department
of my undergraduate alma mater. In part of the newsletter they posed the
following challenge problem:

"For which rational numbers q is 3q^3 + 10q^2 + 3q an integer?"

The problem comes from an annual mathematics competition the school
sponsors.  I fumbled around a bit, using Mathematica v5.2 to attempt an answer,
but without much luck. Of course I'm a statistician, not an algebraist
:-). But my curiosity is now piqued and I was wondering if someone might
outline an elegant answer using Mathematica.

Thanks,

-Mark

• Follow-Ups:
  • Re: Challenge problem
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>