MHB What should I say about elementary number theory?

matqkks
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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?
 
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Chinese Remainder Theorem - always fun. Counting things without actually counting them!
 
tkhunny said:
Chinese Remainder Theorem - always fun. Counting things without actually counting them!
I really like this. Are there any others?
 
matqkks said:
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.
 

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