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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; ... Rational number; Unit fraction;

  3. Diophantine approximation - Wikipedia

    en.wikipedia.org/wiki/Diophantine_approximation

    The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p / q is a "good" approximation of a real number α if the absolute value of the difference between p / q and α may not decrease if p / q is replaced by another rational number with a smaller denominator.

  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. Category:Rational numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Rational_numbers

    Print/export Download as PDF; Printable version; ... Pages in category "Rational numbers" The following 12 pages are in this category, out of 12 total. ...

  6. 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} } .

  7. 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 ...

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