I What should I say about elementary number theory?

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Summary
Motivating talk.
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?
 

Math_QED

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What is your target audience? Did they have a number theory/discrete math course already?

Here is what you can do if they have not really a background in number theory:

Keep things simple!

Everyone can multiply two (big prime) numbers together (given enough time).

But, given a (big) number that is the product of two primes, give an example where it is hard to find the two primes that were multiplied together. Explain that this is in general a very hard problem. No algorithms exist (yet) to find prime decompositions efficiently. Proceed with the RSA principle.
 
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Thanks for this. I will definitely include this in my talk.
 

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