[seqfan] Re: Squares of the form x^2+40y^2 .
Ray Chandler
rayjchandler at sbcglobal.net
Thu Jan 22 23:15:22 CET 2009
Z list appears to be primes p such that p^2 can be represented as x^2+40y^2.
Ray
> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu
> [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Jack Brennen
> Sent: Thursday, January 22, 2009 3:59 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Squares of the form x^2+40y^2 .
>
> It would seem that it contains an infinite number of
> multiples of 1001.
>
> Maybe someone can determine what property of the integer Z leads to
> (1001*Z)^2 == X^2 + 40*Y^2 having other solutions than the 13
> primitive solutions multiplied by Z?
>
> The values of Z which do lead to extra solutions include all multiples
> of:
>
> 7, 11, 13, 19, 23, 37, 41, 47, 53, 59, 89, 103, 127, 131, 139, ...
>
> (Which doesn't appear to be a sequence in the OEIS.)
>
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