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I am a grade 12 student. I am interested in number theory and I am looking for topics to research on.

Can you suggest some topics in number theory and in general that would make for a good research project?

I have self-studied certain topics in Abstract Algebra and Number Theory. I'm fascinated by primes (like most people are).

Preferably, suggest some unexplored problems so that new results can be obtained.

Thanks.

  • 2
    How about finding integer solutions to equations of the form $x^2+y^2=z^2$ ?2012-06-18
  • 1
    Pell's equation (http://en.wikipedia.org/wiki/Pell's_equation)2012-06-18
  • 1
    Investigate (and prove?) divisibility properties of Fibonacci numbers?2012-06-18
  • 2
    I have flagged this to be made into a community wiki.2012-06-18
  • 0
    This might be too broad, but [multiplicative functions](http://en.wikipedia.org/wiki/Multiplicative_function) and interesting/important.2012-06-18
  • 0
    You could take a look at [this question](http://math.stackexchange.com/questions/158595/prime-as-sum-of-three-numbers-whose-product-is-a-cube)2012-06-18

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