I am currently studying number theory, using Kenneth Rosen’s “Elementary Number Theory and its Applications” 6th ed. as the text book. It’s a challenging class, and I’m looking for book recommendations beyond the text book to help me better understand the topics. Specifically, I would love to find number theory books with problems and solutions. Even if someone can just recommend alternative text books that they found useful, that would be helpful as well.

For an interesting and unconventional take on the subject, you might try Oystein Ore’s Number Theory and its History. It has occasional problems but I don’t know if there’s a solution set.

Sounds like you want something like a “Schuam’s Outline” for number theory, but it looks like they don’t have one for that subject, for whatever reason.

There are a lot of good books out there about number theory (just do a search on Amazon), a few of which I’ve read and enjoyed personally; but I’m not familiar with the text mentioned in the OP, so I don’t know which book(s) would be a good complement to it (covering the same things) or have lots of worked-out examples.

If it were me, I would go to your college library (assuming you’re taking the class on campus) and look through the stacks. If your college uses the Library of Congress system, books on number theory are under QA 241 to QA 246. My college library always had a lot of textbooks at various levels, even ones that were never used in class. I think publishers send them to professors in the hope that they would make them the required texts. They mostly ended up in the library. I found them incredibly useful because sometimes the required text explained something poorly, or just in a way that I personally found hard to grasp. Reading the corresponding part of a different textbook often clarified the issue for me.

Note that the main campus library may not be your best bet. Some large campuses have a special library for mathematics, sometimes combined with engineering, computer science, and/or the natural sciences.

It is unfortunately out of print, but when I took Number Theory (in 1956!) we used Wm J LeVeque’s fine book. When I taught the course (around 1990) it was out of print, although I photocopied a number of pages for the students. But if you can find it in your university library, I recommend it. Another book, long out of print is L E Dickson’s classic. I even tried to find who owned the copyright, but it was hopeless. He died decades ago and his wife gave Dover permission in the mid 50s, but she has presumably passed on and Dover had no idea where to go.

I did find a book in 1990, but I won’t mention it since I don’t recommend it.