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@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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