 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 1001111002 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

4748 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.  Thread Tools Show Printable Version Email this Page 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

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