Register to reply

Order of congruence classes

by snakesonawii
Tags: classes, congruence, order
Share this thread:
Apr12-11, 04:14 PM
P: 5
1. The problem statement, all variables and given/known data

If m[tex]\in[/tex]Z and [tex]2\leq n\in Z,[/tex] then [tex]|[m]_n|=\frac{n}{(m,n)}[/tex]

2. Relevant equations

Lagrange's Theorem

3. The attempt at a solution

I am confused simply because it seems like the problem might be missing something. We are asked to find the order of the congruence class m modulo n. But I thought that to even talk about this we must first assume that m and n are coprime. Otherwise we get results like [tex]|[5]_{15}|=\frac{15}{5}=3[/tex]. Yet 5^3=125 which gives you just the class 5 modulo 15 again. If we wanted to look at a cyclic group generated by [tex][5]_{15}[/tex] we would find that it only has two elements, the classes 5 and 10 from repeated multiplication of the class 5, no inverses, and no identity (the congruence class 1 could be an identity but it is never reached by multiplication of 5 to itself).
Phys.Org News Partner Science news on
Fungus deadly to AIDS patients found to grow on trees
Canola genome sequence reveals evolutionary 'love triangle'
Scientists uncover clues to role of magnetism in iron-based superconductors

Register to reply

Related Discussions
Order of Calculus Classes Differential Equations 6
Congruence Classes Linear & Abstract Algebra 9
Congruence Classes Calculus & Beyond Homework 3
Congruence Classes in Quadratic Integers Calculus & Beyond Homework 4
Congruence classes General Math 1