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  2. Casting out nines - Wikipedia

    en.wikipedia.org/wiki/Casting_out_nines

    Casting out nines. Casting out nines is any of three arithmetical procedures: [1] Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to 9 or a multiple of 9. The result of this procedure is a number which is smaller than the original whenever the original has more than one digit, leaves ...

  3. Multiplicative group of integers modulo n - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_group_of...

    n. In modular arithmetic, the integers coprime (relatively prime) to n from the set of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n.

  4. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...

  5. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    The properties involving multiplication, division, and exponentiation generally require that a and n are integers. Identity: (a mod n) mod n = a mod n. nx mod n = 0 for all positive integer values of x. If p is a prime number which is not a divisor of b, then abp−1 mod p = a mod p, due to Fermat's little theorem.

  6. Covering system - Wikipedia

    en.wikipedia.org/wiki/Covering_system

    Hough and Nielsen (2019) [1] proved that any distinct covering system has a modulus that is divisible by either 2 or 3. A covering system is called irredundant (or minimal) if all the residue classes are required to cover the integers. The first two examples are disjoint. The third example is distinct. A system (i.e., an unordered multi-set)

  7. Worksheet - Wikipedia

    en.wikipedia.org/wiki/Worksheet

    In accounting, a worksheet is, or was, a sheet of ruled paper with rows and columns on which an accountant could record information or perform calculations. These are often called columnar pads, and typically green-tinted. In computing, spreadsheet software presents, on a computer monitor, a user interface that resembles one or more paper ...

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