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Re: Simplifying with assumptions

  • To: mathgroup at
  • Subject: [mg48983] Re: [mg48949] Simplifying with assumptions
  • From: Andrzej Kozlowski <akoz at>
  • Date: Fri, 25 Jun 2004 17:52:29 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at

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;

48 - n^2 + 8*x


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

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