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 2018-07-28, 05:14 #1 devarajkandadai     May 2004 31610 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
devarajkandadai

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.

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