Compute the (multiplicative) order of each $[a]_n$.
$[7]_{55}$
Can anyone help me understand how to solve this kind of notation? I am getting confused because I don't know what $[7]_{55}$ means, I thought it meant to solve $7\bmod {55}$ but my answer was incorrect. I am looking for the steps to go about solving this problem.
[7] mod 55 is a congruence class. That is, a set of all numbers x, such that 55 divides (x - 7).
[7] = {(7 - 55n), ... , -48, 7, 62, 117, ..., (7 + 55n)}
Multiplicative order of the congruence class [7] is the power k to which we have to raise 7 in order to get (7^k congruent 1) mod 55