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Old 2004-09-14, 02:35   #1
devarajkandadai
 
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May 2004

22·79 Posts
Default Carmichael Numbers II

A CONJECTURE

Let N = p1p2....pr

The necessary and sufficient condition for N, an r-factor composite number,
to be a Carmichael Number:

(p1-1)(N-1)^(r-2)/ (p2-1)(P3-1)....(pr-1),

(p2-1)(N-1)^(r-2)/ (p1-1)(p3-1)... (pr-1),
.
.

.

(pr-1)(N-1)^(r-2)/(p1-1)......... (p(r-1)-1)

should ALL be integers.

A.K. Devaraj
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Old 2004-09-16, 06:06   #2
devarajkandadai
 
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31610 Posts
Default Carmichael Numbers II

I would be surprised if anyone can show a counter example.

Devaraj
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