For the linear congruence equation http://stuff.daniel15.com/cgi-bin/ma...%5Cpmod%7Bn%7D, the general solution is given by http://stuff.daniel15.com/cgi-bin/ma...7Bnt%7D%7Bd%7D where http://stuff.daniel15.com/cgi-bin/mathtex.cgi?x_0 is a particular solution and http://stuff.daniel15.com/cgi-bin/ma...0=%20%28a,n%29 and http://stuff.daniel15.com/cgi-bin/ma...Cmathbb%7BZ%7D.

My book says for this general solution it forms 'd congruence classes mod n'. What does that mean?

I interpreted it as this:

http://stuff.daniel15.com/cgi-bin/ma...%7Bn%7D%7Bd%7D is always a constant since http://stuff.daniel15.com/cgi-bin/ma...cgi?n%20=%20kd so http://stuff.daniel15.com/cgi-bin/ma...7Bd%7D%20=%20k for some integer constant http://stuff.daniel15.com/cgi-bin/mathtex.cgi?k.

So http://stuff.daniel15.com/cgi-bin/ma...x%20=%20tk+x_0 which can be written as http://stuff.daniel15.com/cgi-bin/ma...%5Cpmod%7Bk%7D which says 'http://stuff.daniel15.com/cgi-bin/ma...%7Bn%7D%7Bd%7D congruence classes mod http://stuff.daniel15.com/cgi-bin/ma...%7Bn%7D%7Bd%7D'

There are http://stuff.daniel15.com/cgi-bin/ma...%7Bn%7D%7Bd%7D congruence classes because http://stuff.daniel15.com/cgi-bin/ma...0x_0%20%3C%20k so there are http://stuff.daniel15.com/cgi-bin/ma...ts%20k-1%5C%7D possible remainders, so there are http://stuff.daniel15.com/cgi-bin/mathtex.cgi?k congruence classes since there are http://stuff.daniel15.com/cgi-bin/mathtex.cgi?k possible remainders.

How did they get 'd congruence classes mod n'?