20050214, 09:28  #1 
May 2004
474_{8} Posts 
Programming a Conjecture
At the outset I must confess that my knowledge of computer programming
is nil. Q: Is it possible to programme my second conjecture on site: www.crorepathibaniye.com/failurefunctions in order to generate Carmichael Numbers? A.K. Devaraj 
20050214, 18:08  #2  
Oct 2004
23^{2} Posts 
Can't access your conjecture
Quote:
Have tried the link you posted and pinging the hostname with no response. Have also tried spelling variations. Please could you check the spelling you typed and revise if needed. Perhaps your server is temporarily unavailable or needs restarting. Alternatively, post an overview of your work in the forum. Once we can view your work we can advise on programming. Regards, Peter 

20050215, 11:02  #3  
Feb 2005
374_{8} Posts 
Quote:
Second, your conjecture can be reformulated as Quote:
It happens that the conjecture works in one direction, namely, for all Carmichael numbers N=p1*...*pr less than 10^7, gcd(p11,p21,...,pr1)^2*(N1)^(r2) is divisable by phi(N)=(p11)*...*(pr1). The opposite is not true in general. There are counterexamples like 11305 = 5*7*17*19 39865 = 5*7*17*67 96985 = 5*7*17*163 401401 = 7*11*13*401 which satisfy the divisibility condition not being Carmichael numbers. Code:
{ test() = for(n=2,10^8, f=factorint(n); if(vecmax(f[,2])>1,next); f=f[,1]; r=length(f); realCM=1; d=n1; for(i=1,r, d=gcd(d,f[i]1); if((n1)%(f[i]1),realCM=0)); if( (((n1)^(r2)*d^2)%eulerphi(n)==0) != realCM, print(n," ",realCM," ",f)) ) } Last fiddled with by maxal on 20050215 at 11:06 

20050215, 13:49  #4 
May 2004
100111100_{2} Posts 
Programming a conjecture
Thank u very much, Maxal.After studying your reply I may have further questions;is it o,k,?
A.K. Devaraj 
20050216, 04:03  #5  
Feb 2005
374_{8} Posts 
Quote:


20050216, 05:10  #6  
May 2004
2^{2}·79 Posts 
Quote:
I am afraid you have not studied the conjecture; it is not only one of the divisibility tests that must be satisfied BUT ALL OF THEM in order to fulfil the "necessary & sufficient" conditions.Kindly try again and you will find that 11305 FAILS one of these tests and hence can be rejected from the list of C.N.S.Regards A.K. Devaraj 

20050216, 06:37  #7  
Feb 2005
2^{2}×3^{2}×7 Posts 
Quote:
Code:
(51)*(113051)^2 / ((71)*(171)*(191)) = 295788 (71)*(113051)^2 / ((51)*(171)*(191)) = 665523 (171)*(113051)^2 / ((51)*(71)*(191)) = 4732608 (191)*(113051)^2 / ((51)*(71)*(171)) = 5989707 And as I stated before, there is a simpler equivalent formulation of your conjecture. Of course, 11305 satisfy its condition as well: gcd(51,71,171,191) = 2 and 2^2*(113051)^2 / ((51)*(71)*(171)*(191)) = 73947, an integer number. Last fiddled with by maxal on 20050216 at 06:39 

20050216, 13:35  #8 
May 2004
100111100_{2} Posts 
programming a conjecture
Dear Maxal,
Yes I did recheck & found you are correct even before u replied to my post. Is there a site where we can obtain all the 4factor Car.Numbrs? Thanking you, A.K. Devaraj 
20050217, 07:47  #9  
Feb 2005
2^{2}·3^{2}·7 Posts 
Quote:
I can generate more if needed. 

20050225, 20:24  #10 
Feb 2005
FC_{16} Posts 
new sequences
Dear devarajkandadai,
I've added two sequences related to your conjecture to OEIS: http://www.research.att.com/projects/OEIS?Anum=A104016 http://www.research.att.com/projects/OEIS?Anum=A104017 
20050309, 02:50  #11  
May 2004
2^{2}×79 Posts 
Quote:
First of all I must thank you for giving my name to the set of numbers generated by my conjecture.Secondly I must thank you for the sequences themselves. Regards A.K. Devaraj 

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