MATH 392
Elementary Number Theory and Cryptography
Winter 2026
Topics
- Representations of integers, induction and contradiction proofs
- Divisibility, gcd, lcm and Euclidean algorithms
- Prime numbers and unique factorization
- Linear Diophantine equations
- Congruences, Chinese remainder theorem and Hensel’s lemma
- Pseudoprimes, perfect numbers and Mersenne primes
- Fermat’s little theorem, Wilson’s theorem and arithmetic functions
- RSA, Diffie–Hellman and digital signatures
- Orders, primitive roots and quadratic residues
- Jacobi symbols, quadratic reciprocity and zero-knowledge proofs
- Pythagorean triples and sums of squares
- Gaussian integers and the congruent-number problem
- Finite, infinite and periodic continued fractions
Readings
- Listed textbook (requirement not stated): Kenneth H. Rosen. Elementary Number Theory, 6th edition.
Winter 2023 · MATH 392
Readings
- Elementary Number Theory, by Charles Vanden Eynden.
Winter 2022 · MATH 392
Readings
- Number Theory Revealed: An Introduction, by Andrew Granville.
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Winter 2026
- Historical course outline ↗Winter 2024
- Historical course outline ↗Winter 2023
- Historical course outline ↗Winter 2022
- Winter 2026 outline.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.