Two conjectures (or are they?):(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Order of an integer

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