Re: Simplifying with assumptions

*To*: mathgroup at smc.vnet.net*Subject*: [mg48983] Re: [mg48949] Simplifying with assumptions*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 25 Jun 2004 17:52:29 -0400 (EDT)*References*: <200406250658.CAA12398@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 25 Jun 2004, at 15:58, Mietek Bak wrote: > Hello, > > I'm a complete newcomer to Mathematica, so please excuse this possibly > silly question. > > I'm trying to determine if a formula will ever give an integer result, > assuming that all variables used in it are integer. I've been > searching > through the built-in documentation, but my best guess didn't really do > anything: > > Simplify[Element[Sqrt[48 - n^2 + 8*x],Integers],Element[{n, > x},Integers]] > > It would be best if I could somehow determine the set of combinations > of > variables that would give an integer result -- if there are any. Is > there a way to do that in Mathematica? > > Thanks in advance, > Mietek Bak. > > > -- > desp; > } > If you want to find just a single solution it is easy: take x = 43; n = 14; then 48 - n^2 + 8*x 196 which is just 14^2. I can also prove that there are infinitely many such solutions. However, I don't think there is any way to solve such problems in general with Mathematica or any other computer program. Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**Simplifying with assumptions***From:*"Mietek Bak" <mietek@icpnet.pl>