Devaraj numbers which act like Carmichael numbers

devarajkandadai · 2018-07-28, 05:14

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.

devarajkandadai · 2018-07-30, 03:44

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.

2018-07-28, 05:14	#1
devarajkandadai May 2004 474₈ Posts	Devaraj numbers which act like Carmichael numbers In the ring of Gaussian integers 33 - 4I = (2 - I)(3+2I)(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.

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