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-   -   Devaraj numbers which act like Carmichael numbers (https://www.mersenneforum.org/showthread.php?t=23538)

devarajkandadai 2018-07-28 05:14

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.

devarajkandadai 2018-07-30 03:44

[QUOTE=devarajkandadai;492624]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.[/QUOTE]

Ignore this as it needs further investigation.


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