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  2. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...

  3. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  4. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    If this infinite continued fraction converges at all, it must converge to one of the roots of the monic polynomial x 2 + bx + c = 0. Unfortunately, this particular continued fraction does not converge to a finite number in every case. We can easily see that this is so by considering the quadratic formula and a monic polynomial with real ...

  5. Algebraic fraction - Wikipedia

    en.wikipedia.org/wiki/Algebraic_fraction

    The numerator and denominator are called the terms of the algebraic fraction. A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the ...

  6. Hilbert's problems - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_problems

    Solving quadratic forms with algebraic numerical coefficients. Partially resolved. [17] — 12th: Extend the Kronecker–Weber theorem on Abelian extensions of the rational numbers to any base number field. Partially resolved. [18] — 13th: Solve 7th-degree equation using algebraic (variant: continuous) functions of two parameters. Unresolved.

  7. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    The terminology used to describe algebraic fractions is similar to that used for ordinary fractions. For example, an algebraic fraction is in lowest terms if the only factors common to the numerator and the denominator are 1 and −1. An algebraic fraction whose numerator or denominator, or both, contain a fraction, such as ⁠ + ⁠, is called ...

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