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  • If you mean properties of numbers such as 'six is triangular' and 'seven is prime' then I would offer number theory as an answer.
  • If you mean that a certain subset of integers derived from the integers by taking remainders modulo a prime form a field then I would offer abstract algebra.
  • If you mean that the integers form a discrete space (the numbers are separate from each other) then I would offer topology.

I would say, poke around at some of the articles on wikipedia with these titles.

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Q: Part of mathematics that studies number systems and number properties?
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