Carmichael Numbers II

devarajkandadai · 2004-09-14, 02:35

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

devarajkandadai · 2004-09-16, 06:06

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

Devaraj

2004-09-14, 02:35	#1
devarajkandadai May 2004 2²×79 Posts	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

2004-09-16, 06:06	#2
devarajkandadai May 2004 2²×79 Posts	Carmichael Numbers II I would be surprised if anyone can show a counter example. Devaraj

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