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!)
- References:
- Re: Integers that are the sum of 2 nonzero squares in exactly 2 ways
- From: Dana DeLouis <dana01@me.com>
- Re: Integers that are the sum of 2 nonzero squares in exactly 2 ways