Fermat's Equation: Integral Solutions and Gaussian Integers

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Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Explores the properties of commutative rings and integral domains in algebra.

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Covers non-degenerate integral quadratic lattices and adèles, including their properties and definitions.

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.