Find integers c≠0, a, b, m such that the solution set of ax≡b (mod m) is different from the solution set of cax≡cb (mod m) Find integers c≠0, a, b, m such that the solution set of ax≡b (mod m) is different from the solution set of cax≡cb (mod m) @Mathematics

Question

Find integers c≠0, a, b, m such that the solution set of ax≡b (mod m) is different from the solution set of cax≡cb (mod m)  Find integers c≠0, a, b, m such that the solution set of ax≡b (mod m) is different from the solution set of cax≡cb (mod m)  @Mathematics

precal · Answer

Modern Algebra - that looks like fun!

anonymous · Answer

Haha.. any suggestions?

precal · Answer

yes I believe all that happened is c got multiplied by both sides.
When you study modern algebra recall your regular algebra except not using mod you can say silly stuff like 1+1=3 as long as you can justify it using a mod.
My Modern Algebra professor got mad once his child got some problem incorrect like 1+1=3 so he was going to go argue with the teacher because he knew he could prove it in some mod.  Anyways it was a corny math joke we got but I am not sure the elementary teacher would have got it or appreciated it.