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>