Fwd: Order of an integer
Sarad AV
jtrjtrjtr2001 at yahoo.com
Wed Jun 1 05:15:49 PDT 2005
--- Cletus Emmanuel <cemmanu at yahoo.com> wrote:
Two conjectures (or are they?):
1. The order of an integer 'a' modulo P^m =
P^(m-1)*(Order of a mod P); where P
is an odd prime .
2. If a, m, and n are elements of Z and (a,mn) = 1,
then Order of a mod mn =
QR/(Q,R); where Q = Order of a mod m and R = Order of
a mod n and (Q,R) is the
greatest common divisor function.
For example:
Example 1:Let a =2 and P=7. Then the order of 2 mod 7
= 3 and the order of 2
mod 7^3 = 7^2(3)= 147.
Example 2: The Order of 2 mod 11^2 = 11*(Order of 2
mod 11) = 110
Example 3: The Order of 2 mod (3*7) = (Order of 2 mod
3)*(Order of 2 mod
7)/(U,V) = 2*3/1 = 6; where U = Order of 2 mod 3 and V
= Order of 2 mod 7.
Are any of these two statements known? If so, could
one point me in the
direction? If not can anyone prove or disprove?
---Cletus
__________________________________
Discover Yahoo!
Find restaurants, movies, travel and more fun for the weekend. Check it out!
http://discover.yahoo.com/weekend.html
More information about the cypherpunks-legacy
mailing list