EulerFoldNumber Theory Fundamentals: From Divisibility to Algorithms
“A four-week, proof-and-code roadmap that moves from integer divisibility and modular arithmetic to congruences, quadratic reciprocity, and cryptographic algorithms. The path emphasizes theorem proving, algorithm design, implementation, benchmarking, and verifiable proof-of-work artifacts.”
Integers, Divisibility, and Modular Arithmetic Foundations
By the end of this module you will be able to prove core integer theorems, implement Euclidean algorithms, and reason rigorously in Z/nZ.
Solving Congruences and Multiplicative Structure
By the end of this module you will be able to solve linear and simultaneous congruences, compute multiplicative functions, and prove Euler-type results for residue rings.
Quadratic Residues, Reciprocity, and Primitive Roots
By the end of this module you will be able to classify quadratic residues, compute Legendre and Jacobi symbols, apply quadratic reciprocity, and analyze cyclic subgroups modulo primes.
Algorithmic Number Theory and Cryptographic Primitives
By the end of this module you will be able to implement primality tests, factorization routines, RSA operations, and discrete-logarithm algorithms with documented correctness and limitations.
References
Week 1: Integers, Divisibility, and Modular Arithmetic Foundations
Week 2: Solving Congruences and Multiplicative Structure
Week 3: Quadratic Residues, Reciprocity, and Primitive Roots
Week 4: Algorithmic Number Theory and Cryptographic Primitives
Community Insights
0Join the discussion
Sign in to share your thoughts and technical insights.
Loading insights...