Hatcher-Topology-of-Numbers · Problem 8.1.10

Quadratic Fields

Mathematics — Algebraic Topology · nonunique-factorization

Problem

(a) Find a number nn that has exactly two different factorizations into primes in Z[−6]\mathbb{Z}[\sqrt{-6}], up to multiplication by units, and find another number that has exactly three such factorizations. (b) Do the same for Z[10]\mathbb{Z}[\sqrt{10}] where things are slightly more complicated since there are many more units.

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