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  2. Hilbert's tenth problem - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_tenth_problem

    Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.

  3. Landau's problems - Wikipedia

    en.wikipedia.org/wiki/Landau's_problems

    Goldbach's weak conjecture, every odd number greater than 5 can be expressed as the sum of three primes, is a consequence of Goldbach's conjecture. Ivan Vinogradov proved it for large enough n (Vinogradov's theorem) in 1937, [1] and Harald Helfgott extended this to a full proof of Goldbach's weak conjecture in 2013.

  4. Basel problem - Wikipedia

    en.wikipedia.org/wiki/Basel_problem

    The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [ 1 ] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences . [ 2 ]

  5. Square-root sum problem - Wikipedia

    en.wikipedia.org/wiki/Square-root_sum_problem

    SRS can be solved in polynomial time in the Real RAM model. [3] However, its run-time complexity in the Turing machine model is open, as of 1997. [1] The main difficulty is that, in order to solve the problem, the square-roots should be computed to a high accuracy, which may require a large number of bits.

  6. Superpermutation - Wikipedia

    en.wikipedia.org/wiki/Superpermutation

    Any hamiltonian path through the created graph is a superpermutation, and the problem of finding the path with the smallest weight becomes a form of the traveling salesman problem. The first instance of a superpermutation smaller than length 1 ! + 2 ! + … + n ! {\displaystyle 1!+2!+\ldots +n!} was found using a computer search on this method ...

  7. Josephus problem - Wikipedia

    en.wikipedia.org/wiki/Josephus_problem

    In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games are used to pick out a person from a group, e.g. eeny, meeny, miny, moe. A drawing for the Josephus problem sequence for 500 people and skipping value of 6.

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