How Can Congruent Mathematics Enhance Number Theory Education?

[matqkks]

What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?

 

[jackmell]

What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?

Encryption. Both RSA and elliptic curve cryptology both use modular arithmetic. If you want it to be interesting, ask your students to google a treasure map in RSA and have them solve it. The modular arithmetic is a bit tough though and would require you give them some background and some sample problems before tackling the treasure map.