KnowraGaussian integerLinked fromLinked fromThe 15 pages that link to Gaussian integer, each with the reason it gives.All 15Broader topic 9Related 6Carl Friedrich GaussBroader topic: Gauss used them to extend arithmetic and clarify when integers can be represented as sums of squares.Ring of integersBroader topic: They form the ring of integers of the quadratic field of rational multiples of i.Unique factorization domainBroader topic: This ring has unique factorization, though its primes differ from integer primes.Euclid's lemmaBroader topic: Their factorization illustrates why ordinary integer primes and divisibility arguments do not transfer unchanged to every ring.Dedekind domainBroader topic: This principal ideal domain is a familiar Dedekind-domain example with unique element factorization.Algebraic integerBroader topic: This familiar ring is an example of algebraic integers inside the complex numbers.Dirichlet's unit theoremBroader topic: Its field has no real embeddings and one complex pair, so the unit rank is zero.Fermat's theorem on sums of two squaresBroader topic: Factoring p as (a+bi)(a−bi) turns a sum of squares into a norm.Brahmagupta–Fibonacci identityBroader topic: The identity shows that products of Gaussian-integer norms remain sums of two squares.