I've recently decided to start preparing for uni, so I figured I need to learn logic and some number theory. I picked up Burton's Elementary Number Theory and wasn't quite comfortable with it, seemed very dry throwing out expressions which I couldn't understand since I'm in still in high school.
Could you recommend me any books on subject which are written in a more approachable manner to a highschooler? I need basics: arithmetic, primes, divisibility, Diophantine, some Fermat maybe.
I also plan on taking some logic. Looking through Tarski's book a little it seemed broad, with not enough emphasis on mathematics. I need some recommendations on that one too. Thank you in advance :)
Peruse these:
You can also find free notes online and the first three are Dover books with great prices.
For gentle logic books, see Logic and set theory textbook for high school.
Also learn to do proofs (cannot be stressed enough), see how to be good at proving?.