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.