I want to know if there are any books that can teach me or introduce me to number theory requiring no prerequisites. This is coming from someone who wants to broaden their mathematical horizons and investigate number theory and cryptology.
Any suggestions are welcome.
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I would absolutely recommend these two books: Number Theory-G.H Hardy, and Introduction to Number Theory - Ivan Niven. The first book sounds a bit outdated at times and has rather strange notation and terminology. I recommend the second book if you want to learn a bit more about quadratic residues and so forth. It is more clear, but it uses less notation and has more "words".
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You don't make it clear what your background is. Some of the other suggestions would probably be good for someone who has at least some experience with proofs. If your background is high school math and this is your first real exposure to proofs, I'd recommend Invitation to Number Theory by Ore.
I taught an undergraduate course in number theory a few years ago using Weissman's An Illustrated Theory of Numbers as the textbook. I think it would probably also work well for self-study. As stated in the preface: "This book has no formal prerequisites beyond high-school algebra and basic coordinate geometry." I found the book to be very well-written, with conceptually clear proofs and lots of visuals to aid understanding.
The topics covered include what I would consider the core of elementary number theory, as well as some topics in quadratic forms that go beyond what I think you would usually see in a first course. There are many historical notes for background and context, and there are also a few sections that explore cryptographic applications, though these are a small part of the book. (If you want to get more into cryptography, I'd recommend supplementing this with a more specialized book on the topic.)