Hi! Recently, I've been playing with some number theoretical problems (just for fun). I've met two similar approches mentioned in the subject: a) P-1 method of factorization and b) N-1 primality test. It seems (if I understand well) that a) we assume that a prime factor p of a given (composite) number n is such that p-1 is smooth; then we can try to determine p itself; b) we _know_ factorization of n-1 and there are some primality tests (see, e.g., Chris Caldwell pages) for n My question is: Is there any method/algorithm to determine _factors_ of n if the factorization of n-1 is known? I understand that there is no _exact_ formula for factors, but maybe there are some strong conditions, which restrict factors to a specific form (like k2^r+1 for Fermat numbers)
The second question I should send directly to Chris Caldwell. In his Prime Pages the N-1 test of primality needs such a that a^(N-1)=1 mod N and a^(N-1)/q is not 1 mod N (q is a factor of N-1). Methods for determining the number a are not presented. Are there any such methods? Regards Wojciech Florek (WsF) Adam Mickiewicz University, Institute of Physics ul. Umultowska 85, 61-614 Poznan, Poland phone: (++48-61) 8295033 fax: (++48-61) 8295167 email: [EMAIL PROTECTED] _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
