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  2. Division algorithm - Wikipedia

    en.wikipedia.org/wiki/Division_algorithm

    Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.

  3. Primality test - Wikipedia

    en.wikipedia.org/wiki/Primality_test

    Since 2 divides , +, and +, and 3 divides and +, the only possible remainders mod 6 for a prime greater than 3 are 1 and 5. So, a more efficient primality test for n {\displaystyle n} is to test whether n {\displaystyle n} is divisible by 2 or 3, then to check through all numbers of the form 6 k + 1 {\displaystyle 6k+1} and 6 k + 5 ...

  4. Chinese remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Chinese_remainder_theorem

    In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1).

  5. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.

  6. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. [44] The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult ...

  7. Integer - Wikipedia

    en.wikipedia.org/wiki/Integer

    The integers arranged on a number line. An integer is the number zero (), a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number ...

  8. Natural number - Wikipedia

    en.wikipedia.org/wiki/Natural_number

    While it is in general not possible to divide one natural number by another and get a natural number as result, the procedure of division with remainder or Euclidean division is available as a substitute: for any two natural numbers a and b with b ≠ 0 there are natural numbers q and r such that = + <.

  9. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes in a fair way between two players, who have to end their game before it is properly finished. [4]

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