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>