On Saturday 04 January 2003 04:08, [EMAIL PROTECTED] wrote: > A Mersenne number M_p = 2^p - 1, where p is prime and p < 1000, > has a prime divisor q with q == 1 (mod 2002) and q == -1 (mod 2001) > [== denotes congruent]. Find q mod 2003.
This problem is ill-defined. There is a considerable number of prime p < 1000 for which not all factors of 2^p-1 are known; indeed there seems to be a set of three such p for which _no_ factors are (currently) known (809, 971, 997). I don't see any reason why any of the missing factors should not have the form stated in the problem. Therefore, even if there is a unique solution based on the currently known factors, this may not remain so as new factors are discovered. For those of you who want to persevere with the problem as stated on the basis of currently known factors: hint, don't forget the cofactor when the published prime factors are divided out; sometimes this is known to be prime. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
