I need help with this problem.
Show that if a and m are relatively prime positive integers, then the inverse of a modulo m is unique modulo m.
[hint: assume that there are 2 solutions b and c of the congruence ax==1(mod m). No need to prove that b==c (mod m) ]
I can fin the solution by starting with the fact that gcd(a,m)=1
--> S*a+ T*m=1 --> S*a+ T*m=1 (mod m) and so on....
But this way of showing this..I don't get it.
I tried something like:
a*b==1(mod m) and c*a==1(mod m)-->a*b==c*a(mod m)
-->b==c (mod m)
then I dont know how to continue..
Can I have some help please?