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[Richard Guy]

Apologies for my wildness.  Mike Speciner
gives the example  n = 8, which generalizes
to any odd power of 2.  Are these the only
examples?  Is the sequence

8, 32, 128, 512, 2048, ... (& including
any other numbers I've overlooked)

in  OEIS ?    R.

On Wed, 22 Jan 2003, Richard Guy 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.
> 
>