The ring of integers modulo n

[jessica098]

Let n be a natural number, and a and b be integers with [a] not equal to [0] in Z[sub:3a9g0n1t]n[/sub:3a9g0n1t] and let d = gcd(a,n). Assume that d does not divide b. Determine the number of solutions of the equation [a]x = in Z[sub:3a9g0n1t]n[/sub:3a9g0n1t]. State a proposition and prove it.

Anybody think they could help me out? Please??

 

[daon]

[a]x= iff n | (b-ax).

So b-ax = nk => b = ax+nk.

You assume d does not divide b, but obviously, d | (ax+nk).

Got it?