--- Cletus Emmanuel <cemmanu@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