What should I say about elementary number theory?

[matqkks]

I need to give an option talk about elementary number theory module. I will discuss how it is study of positive integers particularly the primes and give some cryptography applications. What is a good hook to stipulate in this talk regarding an introduction to elementary number theory?

 

[tkhunny]

Chinese Remainder Theorem - always fun. Counting things without actually counting them!

 

[matqkks]

Chinese Remainder Theorem - always fun. Counting things without actually counting them!

I really like this. Are there any others?

 

[I like Serena]

I really like this. Are there any others?

Counting things without actually counting them?
That brings Burnside's Lemma to mind.
It counts for instance the number of different colorings of a string of colored beads - without actually counting them.