[seqfan] Re: A081650

Emmanuel Vantieghem emmanuelvantieghem at gmail.com
Thu Nov 19 14:18:46 CET 2015


Sure it is.  If m can be written as a product of two relatively prime
numbers u and v, then, a(m-1) is a quadratic residu mod k^2 for k = 1 to
m-1.  Thus, a(m-1) is quadratic residu mod u^2 and mod v^2, thus a(m-1) is
quadratic residu mod (u*v)^2 and thus, a(m) = a(m-1). If m is p^s for some
prime p and s > 2, then a(m-1) is quadratic residu modulo p^2t  for t = 1,
..., s-1. Thus, a(m-1) is quadratic residu mod every power of  p, thus,
a(m-1) is quadratic residu mod m^2 and hence, a(m-1) = a(m)

Emmanuel.

2015-11-19 13:38 GMT+01:00 David Wilson <davidwwilson at comcast.net>:

> Does A260709(n) = A260709(n - 1) for all composite n > 4?
>
> > -----Original Message-----
> > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of M. F.
> > Hasler
> > Sent: Tuesday, November 17, 2015 10:57 AM
> > To: Sequence Fanatics Discussion list
> > Subject: [seqfan] Re: A081650
> >
> > Don, Robert,
> > I edited the title of this sequence to match the data and propose the
> other
> > version as https://oeis.org/draft/A260709.
> > - Maximilian
>
>
>
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>



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