Question related to congruence class equations

[General_Sax]

Homework Statement

3) Let a be an integer = 0 and 6 n a natural number. Show that if gcd(a, n) = 1 then 6
there exists b ∈ Z, such that [a] · = [0] and = [0] in 6 Z/Zn

Homework Equations

The Attempt at a Solution

Ok, so I'm still trying to digest the question and so far I'm going with the fact that if b is a integer multiple of a, ie, b := KONSTANT*a then it should still share a common divisor with both 'n' and 'a'. However, I'm also thinking that b could be --- b := KONSTANT + a. Now, I'm not too sure about the last part, but I think as long as the KONSTANT has a common divisor with [a] and n, then it should still work out. Any comments on my ideas or help in expressing them mathematically?

I'm just not too sure on how to write this up, as I'm not very experienced with 'proofs'.

 

[General_Sax]

that supposed to read a!= 0 and b != 0 ... srry just copy and pasted.