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2. List of number theory topics - Wikipedia

   en.wikipedia.org/wiki/List_of_number_theory_topics

   5 Analytic number theory: additive problems. ... Download as PDF; Printable version; ... Lucas–Lehmer test for Mersenne numbers; AKS primality test; Integer ...

3. Dirichlet's approximation theorem - Wikipedia

   en.wikipedia.org/wiki/Dirichlet's_approximation...

   In his Essai sur la théorie des nombres (1798), Adrien-Marie Legendre derives a necessary and sufficient condition for a rational number to be a convergent of the simple continued fraction of a given real number. [4] A consequence of this criterion, often called Legendre's theorem within the study of continued fractions, is as follows: [5 ...

4. Rational number - Wikipedia

   en.wikipedia.org/wiki/Rational_number

   In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...

5. Dirichlet function - Wikipedia

   en.wikipedia.org/wiki/Dirichlet_function

   For any real number x and any positive rational number T, (+) = (). The Dirichlet function is therefore an example of a real periodic function which is not constant but whose set of periods, the set of rational numbers, is a dense subset of R {\displaystyle \mathbb {R} } .

6. Transcendental number theory - Wikipedia

   en.wikipedia.org/wiki/Transcendental_number_theory

   The question of whether certain classes of numbers could be transcendental dates back to 1748 [2] when Euler asserted [3] that the number log a b was not algebraic for rational numbers a and b provided b is not of the form b = a c for some rational c.

7. List of mathematical functions - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_functions

   Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...