Re: Changing Pure Function in Module

• To: mathgroup at smc.vnet.net
• Subject: [mg29842] Re: [mg29822] Changing Pure Function in Module
• From: Ranko Bojanic <bojanic at math.ohio-state.edu>
• Date: Fri, 13 Jul 2001 04:19:22 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```
Hi Wilson:
Now that we know exactly what you want, it is easy to write a module for FindD:

FindD[n_]:=Module[{c=1,a},If[IntegerQ[Sqrt[n]],a="n is a perfect square",
While[JacobiSymbol[(-1)^(c+1)(2c+3),n]?-1,c=c+1];
a=(-1)^(c+1)(2c+3)];
Return[a]]

FindD[1929321]
n is a perfect square

FindD[567134594567891251143216731]
-15

Regards,
Ranko

In Message 42/124 From Flip at safebunch.com Jul 12,01 02:52:35 AM-0400
Wilson wrote:

> Hi All,
>
> thank you to all who continue to respond to all of my questions ... and there
> are always plenty of them.
>
> I have the following function embedded in the findD code below.
>
> a[1] =5;
>
> a[n_]:= a[n] = (-1)^(n+1) (Abs[a[n-1]]+2)
>
> In[225]:=
> findD[n_]:=
> Module[{c=0},NestWhile[(c++;(-1)^c(Abs[#]+2))&,5,JacobiSymbol[#,n]!=-1&]]
>
> I would like to change the pure function to use the following (cleaner) function
> that requires no starting value (and starts for n = 1).
>
> In[255]:=
> a[n_]:= a[n]= (-1)^(n+1)*(2n + 3)
>
> Also, it would be important to test n prior to calling findD.  If n is a perfect
> square, findD will "never" converge.  Is there a simple way to test if n is
> square and tell the user ... try again ... n is a perfect square.
>
> Again thank you for all of the help ... Wilson
>
>
>

```

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