[math-fun] Re: your mail (fwd)

[Richard Guy]

Thankyou Ed, for correcting the sequence.  R.

---------- Forwarded message ----------
Date: Wed, 22 Jan 2003 09:37:44 -0800 (PST)
From: ed pegg <ed at mathpuzzle.com>
Reply-To: math-fun at mailman.xmission.com
To: math-fun at mailman.xmission.com
Subject: Re: [math-fun] Re: your mail


Numbers less than 100000 with this property are the following:

8, 27, 32, 63, 125, 128, 243, 275, 343, 399, 512, 567, 575, 935, 1127, 1331,
1539, 2015, 2048, 2187, 2197, 2303, 2783, 2915, 3087, 3125, 4563, 4913, 4991,
5103, 5719, 5831, 6399, 6859, 6875, 6929, 7055, 7139, 7625, 8192, 8855,
12167, 12719, 14027, 14375, 14399, 16807, 17303, 18095, 19683, 20519, 20705,
20999, 21125, 21299, 22847, 24389, 24863, 26999, 27783, 28175, 28223, 29315,
29375, 29791, 31535, 32319, 32375, 32768, 33275, 34775, 36125, 38759, 41327,
45927, 46079, 49247, 49619, 50653, 51359, 55223, 58563, 60059, 60543, 63503,
64619, 67199, 68921, 69575, 73535, 74375, 74431, 75087, 76751, 78125, 79507,
80189, 81719, 86975, 88559, 89375, 89675, 90287

--Ed Pegg Jr

--- Richard Guy <rkg at cpsc.ucalgary.ca> wrote:
> I'll make a wild guess that it can be proved
> that no such  n  exists; I'll copy this to some
> people who may be able to confirm or deny this.
> 
> R.
> 
> On Wed, 22 Jan 2003, Mr. Nayandeep Deka Baruah wrote:
> 
> > Dear Professors Guy and Borwein,
> > 
> > I would like to know from you  whether the following result is still a
> > conjecture or has been proved by somebody.
> > 
> > There exists a composite integer n such that for each prime divisor p of n
> > (p+1)|(n+1).
> > 
> > If it is true then what is the smallest such number? Are such numbers are
> > infinitely many?
> > 
> > I would be extremely grateful for your help.
> > 
> > With best regards,
> > 
> > Nayandeep Deka Baruah
> > Dept. of Math. Sciences,
> > Tezpur University
> > Napaam-784028
> > Assam, INDIA.
> 
> 
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