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Old 2018-10-30, 14:18   #2
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May 2004

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Default Carmichael numbers and Devaraj numbers

Originally Posted by devarajkandadai View Post
As you are aware Carmichael numbers pertain to the property of composite numbers
behaving like prime numbers with regard to Fermat's theorem. They are Devaraj numbers
I.e. if N = p_1*p_2....p_r ( where p_i is prime) then

(P_1-1)*(N-1)^(r-2)*(p_2-1)......... (p_r-1) is an integer.
See A104016 and A104017.
a) conjecture: the least value of k, the degree to which atleast two of a Devaraj number's prime factors are
Inverses, is 2 (example 561 = 3*11*17 -here 3 and 17 are inverses (mod 5^2).

b) 5 and 11 are impossible cofactors of Devaraj numbers (including Carmichael numbers).
(to be continued)
C) 7 and 31 are inverses of 3rd degree

Last fiddled with by devarajkandadai on 2018-10-30 at 14:19 Reason: Corrected a slip
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