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## Construct elements of infinite multiplicative order in some quadratic integer rings

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.24 Show that for $D \in \{ 3,5,6,7 \}$ the group of units in $\mathbb{Z}[\omega]$ is infinite…

## The order of conductor f in the ring of quadratic integers is a subring and has index f

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.23 Let $D$ be a squarefree integer, and let $O$ be the ring of integers in the…