<p>I'm currently a Junior in high school, currently enrolled in my school's Math Intel class, which is a research class which requires its students to enter in the Siemens and Intel competitions. I've decided to start teaching myself number theory, as a start, and will switch depending on how much I enjoy the topic. </p>
<p>First: Would this be a good idea to study as a contest entry? (Assuming I have close to no idea on what specific problem/theorem I'd like to study/develop).</p>
<p>Second: I need to find an internship/ math camp to aid me in learning more math, as well as a mentor to guide me. USA/Canada Math camp is now out of the question, because I thought that I'd be able to do all 7 problems in about 2 days... Most of the math internships offered at my school are museum jobs (i.e. they are most likely trash for my purposes). Any idea for a camp/internship to pursue? Currently looking at Bluestamp engineering. (Anything comprised of people who have a heavily problem solving-based mindset. This would include engineers, doctors, mathematicians, physicists, or anything of that nature)</p>
<p>Thank you!</p>