[seqfan] Re: Number of solutions of a*b + c*d + ... + y*z = 0 (mod n)
Ron Hardin
rhhardin at att.net
Mon Sep 6 20:28:04 CEST 2010
----- Original Message ----
> From: Max Alekseyev <maxale at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Mon, September 6, 2010 1:24:34 PM
> Subject: [seqfan] Re: Number of solutions of a*b + c*d + ... + y*z = 0 (mod n)
>
> On Sun, Sep 5, 2010 at 9:10 PM, Ron Hardin <rhhardin at att.net> wrote:
> > How many distinct no-zero solutions are there of a sum of k products of
>pairs
> > of numbers in 1..n-1 such that the sum is zero (mod n)?
>
> Btw, why do you exclude 0?
> Would it be more natural to allow full range of residues modulo n to
> participate in the solutions?
>
> Regards,
> Max
Zeros make the other half of the product free, so you'd be counting
0*0 0*1 0*2 0*3 ... as distinct
Instead, to pick up zeros, adding in nonzero results from fewer products seems
more natural.
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