[seqfan] Re: Finding numbers represented by indefinite binary quadratic forms
Charles Greathouse
charles.greathouse at case.edu
Wed Jun 4 19:30:13 CEST 2014
Dario's applet is very nice though it's worth mentioning that there are
cases he has not implemented (last I checked) and so the applet will give a
'failed' message in those rare cases.
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Wed, Jun 4, 2014 at 10:52 AM, Giovanni Resta <g.resta at iit.cnr.it> wrote:
> On 6/4/2014 4:14 PM, Neil Sloane wrote:
>
>> Dave, Thanks, that Mathematica command does indeed seem to do the job! It
>> gives (as you say) a long list of solutions if solutions exist, and
>> "false"
>> if they don't.
>>
>
> Yes, in general the Reduce command applied to quadratic Diophantine
> equations gives False if no solutions are found, a list of solutions if
> solutions are in finite number, or one or more solutions in exponential
> form, something like
> x == 1/24 (-4 + 2 ((5 - 2 Sqrt[6])^(2 C[1]) + (5 + 2 Sqrt[6])^(2 C[1])))
> with C[1] integer, if there exist infinite solutions.
>
> In case just a few equations have to be solved, there is an online applet
> by Dario Alpern at this address:
>
> http://www.alpertron.com.ar/QUAD.HTM
>
> A nice thing about that page is that it provides also a step-by-step
> solution and that infinite solutions are represented by recurrences
> instead of exponential expressions.
>
> Giovanni
>
>
>
>
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