comments:
It's unclear to me what your background is... you say: During school I studied algebra and geometry ...yet in reply to a comment about finishing (high school) algebra you say that you're just going into 9th grade and so presumably still have more algebra to take in high school? How much algebra you've seen already will limit or expand your options. AoPS has an Introduction to Number Theory textbook that is likely accessible (they claim it only needs basic algebra as a prerequisite), though I don't have it in front of me to check to be certain. On the other hand, if you've finished most of the algebra people usually take in high school, Andrew's Number Theory is a dated but nice introduction to some aspects of "elementary number theory." (It's also inexpensive and does not require any abstract algebra --- note: abstract algebra is a different course than high school algebra --- which I feel makes it a decent first introduction.) A more modern text that is probably more accessible, but I haven't read through the entirety of, is An Illustrated Theory of Numbers --- lots of pictures and emphasis on understanding the "shape" of things and not just systematic proof details, but still assumes a decent familiarity with variables, etc. (Some of the exercises also deal with limits, which are a topic from calculus... though I believe those notions may be skipped and you still get nearly the same benefit out of the book.) When I was about your age (or maybe a year or two older), I didn't have a formalized course in number theory, but I really enjoyed tackling Project Euler problems by reading articles as-needed on Wikipedia and Wolfram Mathworld. It merged an interest in programming with an interest in math, and exposed me to a broad range of topics. As a resource that you might want when you have established more of a background (though I'm a firm believer that it never hurts to at least try watching a few videos before you're ready, since you never really know what someone's limits are), Richard Borcherds has a lecture series on youtube that teaches Berkeley's Math 115, which is an introduction to number theory. Dr. Borcherds is a 1998 Fields Medalist, and has a ton of really useful videos on his youtube channel, ranging from basic introductory courses to intermediate graduate-level topics.