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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 have just started:

a*b==1(mod m) and c*a==1(mod m)

**-->**a*b==c*a(mod m)

**-->**b==c (mod m)

then ??

Can I have some help please?

B