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  2. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r, then the L-function L(E, s) associated with it vanishes to order r at s = 1. Hilbert's tenth problem dealt with a more general type of equation, and in that case it was proven that there is no algorithmic way to decide whether a given ...

  3. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction ⁠ 5 / 7 ⁠ when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...

  4. 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.

  5. Algebraic equation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_equation

    If an equation P(x) = 0 of degree n has a rational root α, the associated polynomial can be factored to give the form P(X) = (X – α)Q(X) (by dividing P(X) by X – α or by writing P(X) – P(α) as a linear combination of terms of the form X k – α k, and factoring out X – α. Solving P(x) = 0 thus reduces to solving the degree n – 1 ...

  6. Bell X-2 - Wikipedia

    en.wikipedia.org/wiki/Bell_X-2

    The Bell X-2 (nicknamed "Starbuster" [1]) was an X-plane research aircraft built to investigate flight characteristics in the Mach 2–3 range. The X-2 was a rocket-powered, swept-wing research aircraft developed jointly in 1945 by Bell Aircraft Corporation, the United States Army Air Forces and the National Advisory Committee for Aeronautics (NACA) to explore aerodynamic problems of ...

  7. Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.

  8. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    For example, taking the statement x + 1 = 0, if x is substituted with 1, this implies 1 + 1 = 2 = 0, which is false, which implies that if x + 1 = 0 then x cannot be 1. If x and y are integers, rationals, or real numbers, then xy = 0 implies x = 0 or y = 0. Consider abc = 0. Then, substituting a for x and bc for y, we learn a = 0 or bc = 0.

  9. Ewers' 5 TD passes lead No. 5 Texas in 49-17 rout of ... - AOL

    www.aol.com/ewers-5-td-passes-lead-204304162.html

    Quinn Ewers passed for 333 yards and five touchdowns and No. 5 Texas rolled over struggling Florida 49-17 on Saturday, two days after third-year Gators coach Billy Napier was given a public ...