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  2. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.

  3. P versus NP problem - Wikipedia

    en.wikipedia.org/wiki/P_versus_NP_problem

    In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O(2 p(n)) time, where p(n) is a polynomial function of n. A decision problem is EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to it. A number of problems are known to be EXPTIME-complete.

  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. Euler's totient function - Wikipedia

    en.wikipedia.org/wiki/Euler's_totient_function

    A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.

  6. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    An illustration of Newton's method. In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.

  7. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    In the first case, the dimension of the solution set is, in general, equal to n − m, where n is the number of variables and m is the number of equations. The following pictures illustrate this trichotomy in the case of two variables:

  8. Binomial coefficient - Wikipedia

    en.wikipedia.org/wiki/Binomial_coefficient

    In 1852, Kummer proved that if m and n are nonnegative integers and p is a prime number, then the largest power of p dividing (+) equals p c, where c is the number of carries when m and n are added in base p.

  9. Pell's equation - Wikipedia

    en.wikipedia.org/wiki/Pell's_equation

    Pell's equation for n = 2 and six of its integer solutions. Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form =, where n is a given positive nonsquare integer, and integer solutions are sought for x and y.