# [seqfan] Re: Squares of the form x^2+40y^2 .

zak seidov zakseidov at yahoo.com
Fri Jan 23 16:13:20 CET 2009

```Just sumbitted.
Is it OK that for any prime^2 there is only one representation
in the form x^2+40y^2?
thx, zak

%I A155488
%S A155488 7,11,13,19,23,37,41,47,53,59,89,103,127,131,139,157,167,173,179,197,
%T A155488 211,223,241,251,263,277,281,293,317,331,367,373,379,383,397,401,409,
%U A155488 419,449,463,487,491,499,503,521,557,569,571,601,607,613,619,641,647
%N A155488 Primes p with property that p^2 is of the form x^2+40y^2.
%C A155488 All p^2 are congruent to {1, 9} (mod 40), as in A107145.
%H A155488 Zak Seidov,<a href="http://zak08.livejournal.com/4251.html">First 1000 terms</a>
%Y A155488 A107145 Primes of the form x^2+40y^2.
%K A155488 nonn
%O A155488 1,1
%A A155488 Zak Seidov (zakseidov(AT)yahoo.com), Jan 23 2009

--- On Thu, 1/22/09, Edwin Clark <eclark at math.usf.edu> wrote:

> From: Edwin Clark <eclark at math.usf.edu>
> Subject: [seqfan] Re: Squares of the form x^2+40y^2 .
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Cc: "seqfans" <seqfan at seqfan.eu>
> Date: Thursday, January 22, 2009, 6:09 PM
> On Thu, 22 Jan 2009, zak seidov wrote:
>
> > Dear seqfans,
> > Is this sequence finite?
> > %S A000001
> 1001,1463,1729,1771,2002,2093,2717,2849,2926,3003,3059,3157
> > %N A000001 Numbers n with property that n^2 has
> exactly 13 representations as x^2+40y^2 with positive x, y.
>
> If Maple's isolve is correct there are lots more n than
> list:
>
> Checking n only up to 10,000 I get:
>
> a:=NULL:
> for n from 1 to 10000 do
> X:=remove(hastype,{isolve(x^2+40*y^2=n^2)},nonposint );
> if nops(X) = 13 then a:=a,n; fi;
> od:
> a;
> 1001, 1463, 1729, 1771, 2002, 2093, 2717, 2849, 2926, 3003,
> 3059, 3157,
> 3289,
>
>    3367, 3458, 3542, 3619, 3731, 4004, 4081, 4186, 4277,
> 4389, 4543, 4807,
>
>    4823, 4921, 5005, 5187, 5291, 5313, 5369, 5434, 5453,
> 5681, 5698, 5852,
>
>    5863, 5957, 6006, 6118, 6251, 6279, 6314, 6578, 6601,
> 6721, 6734, 6853,
>
>    6916, 7049, 7084, 7238, 7315, 7462, 7567, 7579, 7733,
> 7847, 7931, 8008,
>
>    8099, 8151, 8162, 8372, 8437, 8533, 8547, 8554, 8569,
> 8645, 8778, 8855,
>
>    9009, 9086, 9139, 9177, 9361, 9373, 9471, 9499, 9614,
> 9646, 9779, 9823,
>
>    9842, 9867
>
>
>
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>
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