RE: Challenge problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg71213] RE: [mg71123] Challenge problem*From*: "Erickson Paul-CPTP18" <Paul.Erickson at Motorola.com>*Date*: Fri, 10 Nov 2006 06:38:27 -0500 (EST)

In[11]:= Together[ 3q^3 + 10q^2 + 3q /. q -> a/b ] <<Picture (Metafile)>> In[13]:= Simplify[ % /. a -> j b ] Demonstrates that is a is an integer times b, then each of the terms and therefore the sum are integers. It doesn't prove that there are not other solutions - not sure if there are. -----Original Message----- From: Coleman, Mark [mailto:Mark.Coleman at LibertyMutual.com] To: mathgroup at smc.vnet.net Subject: [mg71213] [mg71123] Challenge problem 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