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Re: Integers that are the sum of 2 nonzero squares in

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125794] Re: Integers that are the sum of 2 nonzero squares in
  • From: James Stein <mathgroup at stein.org>
  • Date: Tue, 3 Apr 2012 04:44:45 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201204020824.EAA04222@smc.vnet.net>

On Mon, Apr 2, 2012 at 1:24 AM, Dana DeLouis <dana01 at me.com> wrote:

> Just to point out... even at small numbers, your code shows 325 as a
> solution.
>
...

> However, 325 has 3 solutions. :>(
>
...

> This is 600 more than James had.
> This is due to his code not considering numbers that were equal.  (ie
> {5,5}).
> I believe you considered this valid, as 50 was a solution.
>

Good catch, Dana!  But perhaps not correct. The OP said he was: "trying to
find energy eigenfunctions, with energy proportional to n^2. An
eigenfunction will be a linear combination of all wave functions with the same
energy."

I'm something of an eigenidiot so I may be very wrong, but I suspect that
the linear combinations must employ DIFFERENT wave functions -- no
duplicates, similar to the Pauli exclusion.  Perhaps the OP will enlighten
us...

(At first my code allowed duplicates; I changed it thinking that was a bug!)


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