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2. List of number theory topics - Wikipedia

   en.wikipedia.org/wiki/List_of_number_theory_topics

   Pisot–Vijayaraghavan number. Salem number. Transcendental number. e (mathematical constant) pi, list of topics related to pi. Squaring the circle. Proof that e is irrational. Lindemann–Weierstrass theorem. Hilbert's seventh problem.

3. Number theory - Wikipedia

   en.wikipedia.org/wiki/Number_theory

   Mathematics. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]

4. Transcendental number theory - Wikipedia

   en.wikipedia.org/wiki/Transcendental_number_theory

   Noncommutative algebra. v. t. e. Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways.

5. Algebraic number theory - Wikipedia

   en.wikipedia.org/wiki/Algebraic_number_theory

   Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .

6. Fermat's little theorem - Wikipedia

   en.wikipedia.org/wiki/Fermat's_little_theorem

   Fermat's little theorem. In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In the notation of modular arithmetic, this is expressed as. For example, if a = 2 and p = 7, then 27 = 128, and 128 − 2 = 126 = 7 × 18 is an integer multiple of 7.

7. Apéry's theorem - Wikipedia

   en.wikipedia.org/wiki/Apéry's_theorem

   Apéry's theorem. In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ (3) is irrational. That is, the number. cannot be written as a fraction where p and q are integers. The theorem is named after Roger Apéry. The special values of the Riemann zeta function at even integers ( ) can be shown in ...

8. Non-standard model of arithmetic - Wikipedia

   en.wikipedia.org/wiki/Non-standard_model_of...

   In mathematical logic, a non-standard model of arithmetic is a model of first-order Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the ...

9. Category:Unsolved problems in number theory - Wikipedia

   en.wikipedia.org/wiki/Category:Unsolved_problems...

   Balanced prime. Bateman–Horn conjecture. Beal conjecture. Birch and Swinnerton-Dyer conjecture. Brocard's conjecture. Brocard's problem. Brumer–Stark conjecture. Bunyakovsky conjecture.