mersenneforum.org > Math Devaraj numbers which act like Carmichael numbers
 Register FAQ Search Today's Posts Mark Forums Read

 2018-07-28, 05:14 #1 devarajkandadai     May 2004 13C16 Posts Devaraj numbers which act like Carmichael numbers In the ring of Gaussian integers 33 - 4*I = (2 - I)*(3+2*I)*(4-I) is a Devaraj number ( ref: A 104016 and A 104017 in OEIS ) which acts like a Carmichael number with reference to modified Fermat's theorem excepting when p = 5, 13 and 17 (norms of the three factors). Recall modified Fermat's theorem: a^(p^2-1)==1 (mod p) where a is a quadratic algebraic integer.
2018-07-30, 03:44   #2

May 2004

22·79 Posts

Quote:
 Originally Posted by devarajkandadai In the ring of Gaussian integers 33 - 4*I = (2 - I)*(3+2*I)*(4-I) is a Devaraj number ( ref: A 104016 and A 104017 in OEIS ) which acts like a Carmichael number with reference to modified Fermat's theorem excepting when p = 5, 13 and 17 (norms of the three factors). Recall modified Fermat's theorem: a^(p^2-1)==1 (mod p) where a is a quadratic algebraic integer.
Ignore this as it needs further investigation.

 Similar Threads Thread Thread Starter Forum Replies Last Post devarajkandadai Number Theory Discussion Group 14 2017-11-15 15:00 devarajkandadai Number Theory Discussion Group 7 2017-09-23 02:58 devarajkandadai Number Theory Discussion Group 0 2017-07-09 05:07 Stan Miscellaneous Math 19 2014-01-02 21:43 devarajkandadai Miscellaneous Math 0 2006-08-04 03:06

All times are UTC. The time now is 21:39.

Tue Jan 31 21:39:04 UTC 2023 up 166 days, 19:07, 0 users, load averages: 1.30, 1.17, 1.10