I’m currently self-studying number theory using An Introduction to the Theory of Numbers by Ivan Niven, Herbert S. Zuckerman, and Hugh L. Montgomery. The book includes a large number of exercises, ranging from routine computations to quite challenging problems, with starred problems indicating higher difficulty.
I’m finding it difficult to decide how to approach the exercises effectively. There are too many to attempt all of them, and while some are straightforward, others require more time and creativity. I'm not sure whether I should:
Try to solve all exercises in each section;
Focus only on unstarred (easier) problems to build fluency first;
Prioritize the starred (harder) problems for deeper insight;
Or adopt some other approach altogether.
For context, my background includes real analysis, linear algebra, and multivariable calculus. I never studied number theory before. I’m not preparing for an exam or a math competition. My goal is to develop a deep conceptual understanding of number theory, both for its own sake and to support future study in other areas of mathematics where number-theoretic ideas may appear.