The discussion centers on proving the mathematical statement "ac | bc if and only if a | b." Participants emphasize that while examples can illustrate concepts, they cannot serve as definitive proofs. The proof requires demonstrating that if ac divides bc, then b must also be an integer multiple of a. This involves manipulating the equation bc = k * ac to derive the necessary implications regarding the divisibility of a and b.
PREREQUISITESStudents in higher-level mathematics, particularly those studying number theory or proof techniques, as well as educators seeking to enhance their teaching of mathematical proofs.
You can use examples to disprove a statement (these are called counterexamples), but you can't use examples to prove a statement.aesailor said:Homework Statement
ac | bc if and only if a | b (Note that this is really two implications.)
2. The attempt at a solution
The only way I can see going about this proof is by using examples. I know that in ac | bc the c will cancel out in both, but I don't know how to properly word the proof. Any suggestions would be greatly helpful.