MHB What should I say about elementary number theory?

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SUMMARY

The discussion centers on preparing an engaging talk about elementary number theory, emphasizing its focus on positive integers and prime numbers, along with its applications in cryptography. Key concepts mentioned include the Chinese Remainder Theorem and Burnside's Lemma, both of which serve as intriguing hooks for the presentation. The Chinese Remainder Theorem is highlighted for its fun and practical implications, while Burnside's Lemma is noted for its utility in combinatorial counting without direct enumeration.

PREREQUISITES
  • Elementary number theory concepts
  • Understanding of prime numbers
  • Familiarity with the Chinese Remainder Theorem
  • Basic knowledge of combinatorial principles, specifically Burnside's Lemma
NEXT STEPS
  • Research the applications of the Chinese Remainder Theorem in cryptography
  • Explore Burnside's Lemma and its combinatorial applications
  • Study advanced topics in elementary number theory
  • Investigate real-world examples of number theory in computer science
USEFUL FOR

Mathematicians, educators, students in mathematics, and anyone interested in the applications of number theory in cryptography and combinatorial mathematics.

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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