Relationships of the number kind

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I'm wondering if someone could recommend some number relationships that I could look into.

I don't have loads of math under my belt quite yet. I'm currently in college trigonometry and college algebra. I start my calculus classes next semester and my physics classes the following semester.

I think that stuff is interesting.
I don't really know which relationships to look at, though. Could someone please point me in the right direction? I really just want to discover some of the properties of numbers for myself by working through some simple problems. I just don't know how to get started.

Thanks in advance.
 
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You can read about primes. It is a fascinating topic. How to count them, how to determine if a number is a prime, how to factor composite numbers. You can try to find new patterns of primes ( that will keep you busy for the next 50 years) and if you can predict the next prime, you will get the Fields Medal ( the Nobel for math ). Wikipedia is a good start on the subject.
 
Thank you, epsi00. That DOES sound interesting.
That's exactly the thing I had in mind.
Thank you for the response.
 

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