What's Next?

What's Next

You have implemented the core algorithms of number theory — from the Euclidean GCD to a working RSA cryptosystem. Here are natural next steps:

  • Cryptography — AES, elliptic curve cryptography (ECC), and digital signatures all build on modular arithmetic
  • Algebraic Number Theory — Extend the integers to rings like the Gaussian integers Z[i]\mathbb{Z}[i] and pp-adic numbers
  • Analytic Number Theory — The Riemann zeta function and the distribution of prime numbers
  • Computational Number Theory — Pollard's rho factorization, Miller-Rabin primality, Baby-step giant-step discrete logarithm

Further Reading

  • An Introduction to the Theory of Numbers by Hardy & Wright — The classic reference, elegant and comprehensive.
  • Elementary Number Theory by David Burton — Clear exposition, ideal for self-study.
  • A Course in Number Theory and Cryptography by Neal Koblitz — Bridges pure number theory and modern cryptography.
  • Project Euler — 800+ mathematical programming problems, many in number theory.
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