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some interesting elementary number theory problems 3 (7) The standard way to prove there are in nitely many primes of the form 4n+ 1 is to assume their are a nite number, and let their product P. Another area of interest is to find whether some of the numerous mathematical constants are simple functions of each other. For instance, to this day, no one knows if e + Pi is a rational number or not. Probabilistic number theory. This is a branch of number theory that uses heuristic and probability theory to build conjectures.