I wanted to know applications of arithmetic in $\mathbb{Z}[i]$ that helps in some problems of $\mathbb{Z}$. I found a wonderful set of notes by Keith Conrad. Now I want to read more on a similar topic. I find the generalizations of integers very interesting.
I am looking for some resource on math 'contest' type diophantine equations that can be solved by clever tricks in $\mathbb{Z}[\sqrt{D}]$. What are some good resources on these type of problems?
Thanks guys!