I How to motivate the study of Fermat's Little Theorem

[matqkks]

What is the best way to introduce Fermat’s Little Theorem (FLT) to students?

What can I use as an opening paragraph which will motivate and have an impact on why students should learn this theorem and what are the applications of FLT? Are there any good resources on this topic?

 

[fresh_42]

Who are the students and what do they study? This term is not very specific in American English.

 

[matqkks]

First year undergraduate doing an elementary number theory course and this is there first proof based course.

 

[fresh_42]

How about a test for prime numbers needed for RSA? Class field theory would probably be a bit early.

 

[matqkks]

Okay I will have to look up RSA. The only thing I was aware of was that it used to large primes to make a product n=pq and security is dependent on factorising this large product. Thanks for this.

 

[fresh_42]

Okay I will have to look up RSA. The only thing I was aware of was that it used to large primes to make a product n=pq and security is dependent on factorising this large product. Thanks for this.

I think Shor's algorithm uses little Fermat and yes, RSA needs large primes, so I'm sure Shor is already too slow. But it's a start and a reason for why the primes have to be large! Probability algorithms based on ERH are likely a bit over the edge.